Medication Math for the Nursing Student

Medication Math for the Nursing Student A Brief Introduction to Dimensional Analysis: So what's the big idea, anyway? Take the test: 25 practice problems--have fun with your brain. Review the test with complete answers: Get your intro to dimensional analysis here. Conversion factors for Nursing Students: Copy and make your own cheat-sheet Abbreviations for Nursing Students: Know'm and love'm MedMath Errors and the Nursing Student: Be afraid, be very afraid My Adventures in Med-Math: Or how I came to post so much stuff on this Web site A Guide to Dimensional Analysis: The one-page all-you-really-need-to-know guide How to Minimize Mistakes: You could save a life Dimensional Analysis Summary: A few tips A Critique of Clinical Calculations: A unified approach, 4th ed. Recommended Corrections to Clinical Calculations: A unified approach Dimensional Analysis for everyone else: Some general examples here More examples of Dimensional Analysis: Drug calculations MedMath and your PDA: Files and programs you can use Go to top Medication Math Errors and the Nursing Student A shocking number of patients die every year in United States hospitals as the result of medication errors, and many more are harmed. One widely cited estimate (Institute of Medicine, 2000) places the toll at 44,000 to 98,000 deaths, making death by medication "misadventure" greater than all highway accidents, breast cancer, or AIDS. If this estimate is in the ballpark, then nurses (and patients) beware: Medication errors are the forth to sixth leading cause of death in America. How many medication errors are miscalculation errors? No one really knows since by some estimates as little as one in ten errors are reported (Pepper, 2002). Of reported errors one FDA study (Thomas, et. al., 2001) found that 7% were due to "miscalculation of dosage or infusion rate." Combining this estimate with the estimate for total deaths, as many as 3,000 to 6,800 deaths are caused annually by medication math errors. This would mean that in the average hospital one patient dies every year or two because someone makes a miscalculation, and one or two patients are sub-lethally harmed each month. As future nurses, then, there is a distinct possibility that we will harm, or even cause the death of, a patient over the course of our career. If we believe the adage "first do no harm" applies to us, then what can we possibly do to minimize miscalculation errors? If we only aim to pass Medication Math with an 80% or above, are we setting the bar high enough? It might be late some Saturday night, you're the only RN on the floor, the hospital pharmacy is closed, and it's up to you to calculate a needed dosage. Surely getting the right answer only 80% of the time is not acceptable. Perhaps the problem you need to solve is a little different than any you've seen before or recall seeing in the textbook. How confident will you be that your calculation is correct? The time to build confidence is while we are students. I suggest that as conscientious students we should aim for 95% or better. We should, then, carefully study, learn from, and thereby avoid repeating what mistakes we do make, so that by the time we are working in the real world we can be confident that, if we are vigilant enough, we can approach 100% proficiency. Since "to err is human," we will always be at risk of not achieving a goal of 100% proficiency, but we cannot aim for less, and knowing that we are always at risk will make us extremely careful. Neither effort, desire to avoid error, nor carefulness, however, is enough. We need the right tools and techniques that will help us avoid miscalculations. I believe that dimensional analysis is the most appropriate tool available to us. It is, by far, the best method of solving medication math problems with the least chance of making errors. As nurses we're not likely to ever use whatever algebra, trigonometry, calculus, or statistics we may know and (even better?) we need make no effort to learn these subjects, but we should strive for a deep understanding of, and proficiency in, dimensional analysis (DA). The good news is that mastery of DA is not at all an unobtainable goal. While few could master a vast subject such as algebra in a lifetime, most students should be able to master DA in a few weeks of focused effort. Mastery would mean the ability to solve any problem that could crop up, no matter how it is presented, while avoiding pitfalls, and retaining proficiency in the years to come. Needless to say, if I thought that nursing students were mastering DA, I wouldn't be writing this paper. The bad news, then, is that most nursing students seem to have a weak understanding of DA. Most can follow examples given in the textbook; they can then solve all the practice problems that follow the same general format. If quizzes or tests also follow the textbook examples, most students succeed brilliantly. That all is not well, however, is apparent went problems do not meet expectations. One sophomore class stumbled badly on a test apparently for this reason. They could all follow, if imitatively, the examples in the textbook, and could therefore do all the practice problems, but when the test presented problems in an unexpected format, most failed--only 2 students passed the test. In their final semester before graduating as RNs, a third failed another test. This suggests a weak understanding of DA. Unfortunately most students have almost, but not quite, a complete understanding of DA. I believe this is due to the textbook used (Clinical Calculations: A unified approach, 4th ed.) almost, but not quite, presenting a complete description of DA. It may be that there are too few nurse/mathematicians to write textbooks, and so a weak foundation for DA is laid for students to build on. My aim in writing this paper is to provide nursing students with a more robust foundation to build on, and perhaps reduce future misadventures. I am not a mathematician, but I have been doing DA for 30 years, have made refinements in the technique over that time, and as a substitute teacher I have taught it to middle and high school students. Dimensional analysis is your friend. Embrace it; learn to love it. It is our best defense against doing harm to a patient by miscalculation. Go to top My Adventures in Med-Math I did my first med-math problems when my wife was in nursing school. She's pretty sharp and no math weenie, but some problems proved frustrating and she'd say, "Okay Mr. Math Guy, see if you can solve this one." I'd do the old bing-bang-boom, and offer up the (correct) answer. Once I got the old, "Ha! You're wrong, the answer key says it's ..." to which I helpfully replied, "When you go to class tomorrow be sure to let your instructor know her answer key needs correction." Somehow I gave the impression of being some sort of math whiz, which I knew not to be the case, but damned if I was going to admit it to her--I didn't want her thinking she was smarter than me in everything! Unfortunately, at the time, I didn't pay any attention to how nursing students were being taught to do med-math, and she, asking only for the answer, paid no attention to how I so easily and annoyingly came up with the right answer every time. As it happened, during her first year she was taught the traditional (for nurses) approach using ratios, proportions, and formulas. Then during her second year, the school switched over to the new fangled (for nurses) approach based on dimensional analysis. A couple of years later our daughter started nursing school (I started the next year), and I got to hear all the med-math horror stories about how many did or didn't pass the latest med-math quiz (these were given throughout the year after everyone had passed the 8-week med-math class) and had to attend remedial classes (on the dreaded titration quiz only two students in her class passed the first time!). Unfortunately, once again, I didn't look into how she and other nursing students were being taught to do dimensional analysis. I just thought there was something about medmath problems that made them incredibly difficult to solve. I should have known that there was something horribly wrong. I had learned to do dimensional analysis (DA) some thirty years earlier when I was taking a lot of chemistry classes. I've happily used DA ever since and had never encountered an applied math problem in chemistry, physics, or engineering that DA couldn't readily dispatch, and yet I was willing to assume that med-math problems, with the exception of the ones I had done myself, were somehow different and intrinsically harder. I'm such a bloody moron! It wasn't until I started nursing school and took the obligatory med-math class that I finally realized what was going on. I had an hour or so to kill before the first class, so I opened the textbook to glance through it. Before class began, I had realized, with growing shock and disbelief, that the authors of the textbook didn't understand the technique they were attempting to teach to nursing students. There were serious errors of omission--things you really need to know to do DA right and well. And there were serious errors of commission--using techniques and the language of math so badly as to give the text a distinct air of innumeracy. I was convinced that if I had had to learn DA from this book, I would be at serious risk of not passing the class. My next thought was, "Hmm, wonder where the instructor learned to do DA?" So here I was in an 8-week class with nothing to do apart from memorize a few abbreviations and conversion factors. The instructor made a good show of pretending she knew what the textbook was talking about. Instead of risking doing problems on the board herself, she deftly had students, a half dozen or so at a time, come up to the board to do problems from the text. Then she would point to each problem in turn and ask if everyone got the same answer. If anyone thought the answer wrong, they got to explain how they came up with the right answer. This actually worked out rather well as several students had enough sense to ignore the textbook and figure out how to do the problems in spite of the book. Since I had a lot of spare time, I decide to see if I could do something to improve the situation. Perhaps a critique of the text with suggested corrections would help. Better, I could explain how I was taught to do DA with the gentle hint that maybe the Ph.D. chemist who taught me understood DA better than the nurses who wrote the textbook. I got started, getting my thoughts together in writing, that first week of class. Part of the situation was that here's a freshman nursing student, O ye of zero credibility, seriously thinking about calling into question the mathematical acuity of textbook authors with advanced degrees (in nursing), and implying that those teaching or who have taught the class, having learned DA from the book, didn't quite know what they were doing either. I needed to be careful and make sure I knew what I was doing. My first reality check was to mention my assessment of the textbook to a fellow student known to have a good grounding in science and math. He immediately agreed that the authors were confused, but as he was doing fine, he didn't seem interested in offering any corrections--a wiser man than I. I felt that my critique and suggestions should stand on their own merit. They thanked me for the offer. they would at last master med-math by the book. working on another project--something about a theory of everything. I assured them I could help. but decided not to risk being confused any more than they already were. but Jef is the creator of the Macintosh computer and was lead designer of the Mac OS. Basically he agreed that the authors' presentation of DA was "illogical and incorrect. and they just weren't getting it." But he went on to explain that gifted scientists and mathematicians use a different technique. but from there on I pretty much did my own thing. and since then. I needed to consult with someone whose mathematical acuity was beyond reasonable doubt. he has written over 300 articles and books on science. and to tough it out in the hope that. I sent Jef copies of the textbook. with enough effort. and I'd invite all the faculty listen to my presentation. They were taking it again and knew they'd be dropped from the program if they failed again. There were others more willing to let me confuse them. I was prepared to argue my points based on evidence and reason. I thought of spinning my work into an Honor's Project. and technology issues. I recall two who had taken the class over the summer and had failed it. I didn't mention my correspondence with Jef to my project mentor or other faculty. and reported the next day that she tried my technique out on various problems the night before and that it worked! She later mentioned getting 100% on the final. and even I found it difficult to consider the possibility that I might be right. Jef Raskin may not be a household name. One student asked me a couple of days before the final how to pick a starting factor (something the text fails to mention). I emailed Jef Raskin about my problem who replied that he was a strong supporter of DA and was willing to help. math. which would involve some faculty involvement and oversight.The only students to get in serious trouble were the ones who spent way too much time reading the book. This approach. At the end there would be an Honor's Colloquium. Of course. Sadly. and as a bonus his wife is a nurse with advanced degrees (which is what made me think he'd take an interest). Steven Hawking was too busy. Problems are approached from first principles and reasoned through to the answer that makes sense. or so he claimed. and felt that to play the Authority Card to gain credibility would . namely none at all. is slow and error is a risk. I was given the nod to go ahead. Ideally I wanted someone whose math ability was off the scale. so I had to find someone else. It was a pleasure and a privilege to correspond with Jef. but the aim is to understand deeply and not merely crank out the right answer using some superficial technique. Prior to that he was a professor of computer science at UCSD. so he could form his own opinion. superficial technique that gives us the right answer every time looks pretty darn good. someone whose judgement I could completely trust. The instructor tried without success then asked me to tutor them. apart from being known widely as a human interface guru. for those of us less gifted folk. The pressure was on. I really like this guy. those portions I found questionable. these were the two who were dropped because they couldn't pass med-math. but all reported that my clairifications were helpful. the think-it-through technique. but that I wasn't going to teach them to do DA the book way. I realized that my presumptuousness was off the scale. As the hours put in to the project began to mount up. but one can always hope. Needless to say I had plenty to say on that point." attached to them. I personally invited the Director of Nursing and any faculty who might be interested to attend. then add others until all the units you don't want cancel out and you're left with only the one or ones you do want (which is why you determine the answer units first). and that all points were taken. pick a logical factor to start with. As my first year of nursing school came to a close.be in bad form. I hope someone out there is being helped. You pay attention . When all the students at the college who had done Honor's Projects were scheduled to present. no one from the nursing department was able to attend. or "dimensions. She was receptive. and here I must note that I detected or imagined some annoyance on her part that I was bringing up the subject yet again. Unfortunately. My presentation went well and was well received by the 30 or so academics present. I posted some stuff on a Web site. I contacted by email the instructor currently teaching med-math (not the one I had had). Go to top A Brief Introduction to Dimensional Analysis When you're doing applied math. Someone noticed that when you plug values into a formula and pay close attention to what happens to the units as the formula is simplified. This process is fairly trivial. numbers have units of measure. I don't know if med-math students are doing any better as a result. At any rate she never called and I never offered again. I told the Director of Nursing I would be willing to meet with her and any interested faculty to explain my concerns about the med-math program at a time of their convenience. and with only slight attention to detail. This always happens if the formula is correct and you plug in the appropriate factors. you always get the right answer. I was the only nursing student on the list. So then someone figured out that you don't need formulas at all. The technique has been taught to students of applied science for longer than I have been able to determine and for the sole reason that students using it make fewer mistakes. and shamelessly played the Authority Card. She said she'd let me know. In hindsight I probably should have in order to gain enough credibility to be listened to in the first place. I was given time to make my case. due to schedule conflicts. felt I was listened to. At the end of my final year of nursing school I felt I had an ethical responsibly to try again. mentioning straight off that she had already come to the conclusion that there was something not quite right with the textbook. but had yet to determine what it was. This got me a meeting. On the off chance that someone out there in cyber land would be interested in my work. For every problem you can just take the factors associated with it. you'll see that most of the units cancel out and you're left with only those units that end up in your answer. error is not an option. e. Determine what you already know. 1.g.g. but coming up with the right answer only four out of five times isn't good enough. Passing med-math may require getting 80% of test problems right. Rephrase if necessary using "per. Think: "Drip rate is 45 drops per minute. While not all steps listed below will be needed to solve all problems. "how many milligrams are in a liter of solution. e. Determine conversion factors that may be needed and write them in a form you can use. a. Translate into "math terms" using appropriate abbreviations to end up with "mg/L" as your answer unit (AU). While mistakes can still be made using any technique. Go to top A Step by Step Guide to Dimensional Analysis The following summary can be used as a guide for doing DA.  Factors from a conversion table: If the table says "to convert from lb to kg multiply by 2. 25%. As nurses doing calculations. Read the problem and identify what you're being asked to figure out.g. See the answers to the self test for a detailed explaination of DA. you have a major clue you're doing something wrong and that your answer is guaranteed to be wrong. you counted 45 drops. Some familiarity with DA is assumed. Setup the problem using only what you need to know." b.2 lb/1 kg" as conversion factors you may need. "45 gtt/min"  If a given is in the form mg/kg/day.g. e. Write this down." a."  Translate into math terms using abbreviations. Determine what you want to know."  Rephrase if necessary.2 lb" and/or "2. dimensional analysis does the best job of minimizing them. if anything? Example: "In one minute. See example 1. so write down "1 kg/2.2 lb. such as "60 min/1 hour. "AU= mg/L" 2.to the units of measure and if they're not canceling out right." Example: You want to know "milligrams per liter." You will need enough to form a "bridge" to your answer unit(s). What are you given by the problem. I have found that any problem that can be solved using DA will yield its answer if the following steps are followed. rewrite as 25/100 with appropriate labels (see example 5) b. I would not suggest memorizing the sequence of steps. e.2 lb/1 kg" 3.2. . Perhaps The Math-Weenie NoBrainer Technique would be more appropriate. rewrite as mg/kg x day (see example 4)  If a percentage is given.  Factors known from memory: You may know that 1 kg = 2. but rather understanding and practicing them." then write down "2. The only fault lies in the name. Understanding is more durable than memory. Compare units in answer to answer units recorded from first step. then comparing the answer to the first one. If the same number is on the top and bottom. See example 1.  Or pick a factor that is given. See example 6. b.735. A more realistic answer would probably be 74. then do the math. Keep picking from what you know factors that cancel out units you don't want until you end up with only the units (answer units) you do want. Go to top . This is a fairly bare outline. Multiply all the top numbers together. a. Take a few seconds and ask yourself if the answer you came up with makes sense. Add labels (the answer unit) to the appropriately rounded number to get your answer. See example 9.73 + 0.a.  If possible. setup as a separate sub-problem.733333 to 74.  If you round to a whole number that implies a greater accuracy than is appropriate. start over. If it doesn't. rather than read. e. Miskeying is a significant source of error. or 74.  Note that the starting factor will always have at least one unit not in the desired answer unit(s) that will need to be changed by canceling it out. Pick from what you know a conversion factor that cancels out a unit in the starting factor that you don't want. cancel them out.7 mL or 75 mL. so refer to Appendix A for examples. Double check to make sure you didn't press a wrong calculator key by dividing the first top number by the first bottom number. b. Round off the calculated answer.73 mL that implies that all measurements were of an extreme accuracy and that the answer is known to fall between 74. c. try picking a different starting factor. If you can't get to what you want. write your answer to indicate a range. 5. d. Pick a starting factor. or checking for a needed conversion factor. See example 1.005 mL. alternating until finished. d. If an intermediate result must be rounded to a whole number. Simplify the numbers by cancellation. Solve: Make sure all the units other than the answer units cancel out. The steps are best taught. so always double check. then divide into that number all the bottom numbers. then use the rounded off answer as a new starting factor. pick from what you know a factor having one of the units that's also in your answer unit and that's in the right place.725 and 74. 4. such as 75 + 5 mL. such as what the physician ordered.  Be realistic. If you round off 74. solve. and so would serve better as a guide to tutoring students than as a self-teaching guide. c. such as drops/dose which can only be administered in whole drops. See example 9. e. so we must be very clear about what we want. An error of omission is less likely using the following non-fraction format: This format is more visually integrated. When written in factor form using bars. like me. mistakes and confusion are minimized: This is. 2/3 is not equal to 3/2. even though they are factors and shouldn't be confused with fractions. then dividing by 50 and 500. circle it in the problem. Should we just keep the answer unit in mind. more bridge like. the first number can be overlooked. can make a difference. Reading the problem with the sole. but eventually you'll blunder because of poor technique. How we choose to write down a DA problem. focused purpose of determining the answer unit. then writing it down (least we forget or get confused later on) is an example of good technique. Since the first factor is normally multiplied. DA problems are often written in fraction form. another reason to avoid the fraction format. the horizontal bar means "divide. It is also less confusing when doing amounts-per-body-weight-per-dose or day calculations. . In this format. or actually write it down? At best we will hit what we aim for. You'll triumphantly.How to Minimize Mistakes Anything we can do to reduce errors by even the smallest degree is worth doing. instead of multiplying 250x50x1000. an error.3 mL/min" as your answer forgetting that you were supposed to calculate "mL/hr" and all because you neglected to write down the answer units and compare them with your answer. especially if you're using scratch paper with other problems on it." and vertical bars mean "multiply. write down "4. and is more appropriate for working with factors. then. about the answer unit(s) we are aiming for. while factors can be (3 tsp/1 tbs is equivalent to saying 1 tbs/3 tsp." Occasionally a factor like "50 kg" will need to be divided rather than multiplied which could cause confusion or errors when doing the math if the division sign is not noticed when written in fraction form. for example. When it comes time to do the math. You can be sloppy and still get the right answers most of the time. students might stumble if division is required and divide everything into 50. perhaps because it is visually different and not in line with other values. Fractions cannot be inverted and remain correct. Writing "25 mL NS" is much clearer than just "25 mL. then. With practice all nursing students can acquire a high level of proficiency in doing medication math. B." If you were doing calculations involving milliliter volumes of three solutions. R. always start with a zero. it is advisable to actually write down. failure to fully label numbers can lead to serious confusion and error. and not 5U insulin. When writing numbers less than one. so write 0. Eric Lee. It may therefore be helpful to label fully rather than minimally. A. in "math terms" or factor form anything given to you by the problem as well as any conversion factors you had to look up. but we can minimize the number of errors we make. the brain is looking for numbers and could see "10" where a "1" is meant: Avoid "cc" and use "mL" instead as cc can look like zeros. The preferred abbreviation.Perhaps with the exception of conversion factors you have memorized. is "mc" for "micro" as in "mcg" for "microgram. always be aware that you are dealing with grams of something or liters of something. Likewise don't use U for unit. RN busybee@alysion. then do not use "mL" alone without specifying "mL of what?" Your labels. When writing whole numbers omit writing a point zero to indicate that the measurement was made to the nearest tenth (or point zero zero to indicate an accuracy of plus or minus a hundreth) as you would in science lab. Conclusions Errors may be unavoidable in absolute terms." In some problems.4 and not . Using a degree symbol for hour instead of "hr" is an invitation to error.4 as the point could be overlooked. Another abbreviation to avoid is using Mu ( µ ) for micro as in microgram (µ g). would be in the form "23 mL A" or "3 mL C" and you would know to only cancel out "mL B" with "mL B. Use abbreviations that are clear and label numbers fully. A good understanding of dimensional analysis is our best defense against miscalculation errors.0 could be mistaken for 50 if the point were over looked. and C. which could be mistaken for 50. If the degree symbol is written a little too big it could be mistaken for a zero resulting in an order of magnitude error. "µ " can look like an "m" and so "µ g" looks like "mg" which could lead to a three orders of magnitude error. When doing the math. Often the hardest part of a problem is translating fuzzy English phrasing into crisp math terms you can use." Whenever you label any number with a unit of measure. In med-math a hand written 5. and so on. then. Write 5 units insulin. When handwritten.org . 1 7/8 = 15/8 4.35 . (Oct. Available online: http://www4. 10 1/5 .nas.edu/news. Available online: http://www. ask if you can take the final. Hoquist C. Drug Topics. 16/5 = 3 1/5 3.References Institute of Medicine (2000) To Err Is Human: Building a Safer Health System National Academy Press.ashp. 2001) Med error reports to FDA show a mixed bag.html Thomas MR. General Math Which of the following statements are True? 1. 2/3 + 3/4 = 19/12 5. Each problem is a mini-test of some important concept. 145(19).pdf Go to top MedMath Practice Problems for Nursing Students The following problems will test your math ability without wasting your time with repetitive problems.fda. 1. 5/8 ÷ 1/16 = 10 9.gov/cder/drug/MedErrors/mixed. Ginette A. (2002) Errors in drug administration by nurses from Understanding and Preventing Drug Misadventures Conference. 20/48 = 5/12 2. 35% = 0. Phillips J. 7 1/8 x 3/4 = 5 11/32 8.nsf/isbn/0309068371? OpenDocument Pepper. review the underlying concept.6 3/5 = 3 3/5 7. 23. If you miss any question.org/public/proad/mederror/pep. Available online: http://www. If you get them all right. 5/9 + 2/3 = 1 2/9 6. You are to give "gr 5 FeSO4" but the available bottle gives only the milligrams of iron sulfate per tablet (325 mg/tab). how many seconds are in a day? 2. You just opened a 500-mL bottle of guaifenesin and will be giving 1 tablespoon per dose. Your order is for meperidine (Demerol) 35 mg. Just as a warm up. On hand are 1 cc and 3 cc syringes. You give your home health patient an unopened 500-mL bottle of guaifenesin and tell them to take 2 teaspoons 4 times a day as ordered. How many doses are in the bottle? In other words how many tablespoons are in 500 mL? 4. this and several of the other problems are ones I've actually encountered in my nursing practice. How many milligrams is the order for? (Yes. xiv = 14 See Answers Dimensional Analysis Problems (see Conversion Factors for Nursing Students) 1. STAT. How much should you draw up into which syringe? . Available is a 2-mL vial containing 50 mg/mL meperidine.10. They ask you how long the bottle will last.) 3. IM. 5. 2 mg MS in 5 minutes. At what rate should you set the pump? 9. Your hospice patient is on a double pump. It occurs to you that you could reset the pump to deliver 0. a 0. according to the textbook.5 g baking soda. You are shadowing a nurse during a clinical who receives an order to adjust the infusion rate of a pump so that 1. On your first day of clinicals at a long-term care facility you are caring for a resident receiving total enteral feeding through a PEG tube. but admits that at the moment her brain doesn't seem to be working.6. 2.2 mL IV push. the nurse tries to solve the problem on a calculator. but on looking in the narcotic cabinet you find none available and the pharmacy is closed. You decide to adjust the drip rate accurately to give the ordered amount. His over-extended regular nurse hangs drip tubing. She assures you she can always do problems like this on tests. 2. He is receiving 60 mL Jevity per hour as ordered when the pump fails and no other pumps are available.4% solution.5 g salt. The answer. and the other has a 100 cc bag containing 2 mg morphine sulfate (MS) running at 5 cc/hr for pain management. A textbook on clinical calculations includes the following conversion for household to metric: 1 teaspoon = 5 mL = 5 g. One side is running NS at 30 cc/hr KVO. After the fifth different and incorrect answer you find a piece of scratch paper and offer to show her how to set up the problem. 30 g sugar. How would you set up and explain the problem to her? 7.2 mg MS STAT. adjusts the drip rate to something that "looks about right. What do you need to know to do so? 8.6 mg of lidocaine are being delivered per minute. As a home health nurse you need to help a client make homemade pediatric electrolyte solution using the following recipe: 1 L boiled water. She begins to show signs of breakthrough pain and her doctor orders 0." and rushes on to her next demand.4 grams lidocaine. then go back to 5 mL/hr. 1. Without writing anything down. Hanging is a 100 cc piggyback containing 0. You would normally use a prefilled syringe containing 1 mg/1 mL MS and give 0. Since only kitchen measuring cups and spoons are available you need to convert from metric.5 g lite salt (KCl). is 1 qt boiled . What error did the textbook make? 11. and 1/2 tsp baking soda. 2 tbsp sugar. No pump is available. the set up is not. 1/2 tsp lite salt.water. In a home setting. Directions: Reconstitute with 10 mL sterile water for injection to yield 100 mg/mL. but the tubing set package notes that the drop factor is 10 gtt/mL. How may mL of Chloromycetin should be administered? Equivalents: 1 g = 10 mL. In another textbook you are given the following example: The order is for Chloromycetin 300 mg IV bolus via saline lock. how would you prepare 1 L (or so) of normal saline (0. 13. 12. How would you adjust the drip rate? . You have an order to infuse 1000 mL of D5W (5% Dextrose in water) IV over a period of 5 hr. 1000 mg = 1 g 300 mg x 1000 mg 1g 1 g x 10 mL = 3 mL While the answer "3" happens to be right. 1/4 tsp salt. What questionable assumption does the textbook make? 10. Label: Chloromycetin 1 g. How would you prepare 2 L of 3% sodium hypochlorite (bleach) and water solution? You have only a measuring cup.9% NaCl) using water and table salt if you have only a measuring cup and a teaspoon? On hand is an unopened 1 lb box of salt. The order is for amoxicillin 60 mg. How much heparin has been given? .14. Available is Tagamet 300 mg in a 2 mL vial of aqueous solution. How much of each will you draw up? 15. The pediatric dosage range is 20-40 mg/kg/day in three equal doses. IM. You are to dilute a portion of this in 100 mL NS and infuse over 20 minutes using a Buretrol with a drop factor of 60 gtt/mL. A child with severe poison ivy weighs 25 kg and Benadryl po 5 mg/kg/day is ordered q6h. What dose should be given? 18. and what will the drip rate be? 16. The two are compatible so you plan to draw up both in the same syringe. Is the dose safe? 17. Tagamet is ordered 200 mg.5 mg/5 mL solution. You are to infuse heparin 5000 U in 250 mL NS at 30 mL/hr. q6h. tid for a child weighing 13 lb. What is the concentration of heparin solution? When you clear the pump you note that 187 mL have been infused. The order is for meperidine 60 mg and atropine gr 1/150.4 mg/mL. Benadryl is available as a 12. IV. How much Tagamet will you inject into the Buretrol. The meperidine on hand is 100 mg/mL and the atropine is 0. po. Your patient weighs 155 lb. • What is the concentration of the solution in mcg/mL? • How many mcg/min. You are to give Lidocaine 30 mcg/kg/min to a child weighing 55 lb.29 m2. Phenobarbital 180 mg/m2/24 hours given every eight hours is ordered for a child whose BSA (body surface area) is 0. The range is 3-6 mcg/kg/min. Available is Nipride 50 mg/250 mL. How much will each dose be? 21. could be administered? . A microdrip chamber (60 gtt/mL) is used with a pump. The piggyback contains 120 mg Lidocaine in 100 mL NS.19. lower and upper range. and you are ordered to infuse 250 mg dobutamine in 500 mL NS at 10 mcg/kg/min. At hat rate will you set the pump? 22. Nipride is ordered and you are to titrate to maintain the systolic blood pressure at 150 mm Hg. How many milligrams of dobutamine will infuse per hour? 20. Your patient weighs 143 lb. how many mcg/min will the patient be receiving? • After 1 hr.9 milliscruples of Morphine IV for each stone of body weight to be administered over a 300-minute period. then use the Back button on your browser to return. Is the ordered dose safe? (Yes. Available is 1 gill of Morphine (MS) solution having a concentration of 0.8 to 10 mg of morphine can be given per hour. At what rate should you set the pump? Your drug guide says that 0. all the units of measure are real.• Within what range will the pump rate be set? • What is the titration factor in mcg/gtt? • The patient's systolic BP is currently 170 mm Hg while receiving the low range dose. If you increase the gtt/min by 5 gtt. so you decrease the gtt/min by 6 gtt. just how to get from what you are given to what you want to know. if seldom used. the systolic blood pressure is 120 mm Hg. The patient weighs 79 kilograms. Dr.) . See the long list of Conversion factors for clues.4 pennyweights of Morphine dissolved in 1000 drachms of solution. orders 1. wishing to test your perspicacity. How many mcg/min is the patient now receiving? 23. but the point is you don't even have to know what the units are. How would you prepare 500 mL of a 1:35 bleach solution from a 1:10 bleach solution using water? 24. Kissoff. You test the eyedropper and find there are actually 64 drops in a teaspoon. She gives you an eyedropper bottle labeled: Take 1 drop per 15 lb of body weight per dose four times a day until the geebies are gone. You have come down with a bad case of the geebies. You are going on a three-week trip and are deeply concerned that you might run out of granny's geebie tonic. Do you need to see her before leaving to get a refill? . and the 4-oz bottle is half-full. but fortunately your grandmother has a sure cure. 60 drops=1 tsp.25. Contains gr 8 heebie bark per dr 100 solvent. You weigh 128 lb. am = before noon (ante meridian) AMA = against medical advice aq = water AS = left ear (auricula sinister) AU = both ears (auriculi utro) bid = twice a day (0900.Go to top Abbreviations for Nursing Students Units of Measure c = cup cc = cubic centimeters cm = centimeters dr = drams dss = 2 teaspoons fl = fluid ft = foot g = grams gal = gallon gl = glass gr = grains gt = drop gtt = drops in = inches kg = kilograms L = liters lb = pound m = meters mcg = micrograms mEq = milliquivalents mg = milligrams mL = milliliters mm = millimeters oz = ounce pt = pint qt = quart tbsp = tablespoons tsp = teaspoons U = unit Other Abbreviations a = before (ante) ABG = arterial blood gas ABT = antibiotic therapy ac = before meals (ante cibum) AD = right ear (auricula dexter) ADH = antidiuretic hormone ad lib = as desired ADA = American Diabetes Ass. 1700) BP = blood pressure BUN = blood urine nitrogen c = with cap = capsule CAD = coronary artery disease . 1700. 0600. 1300.. 1400. 1800) q8h = every 8 hours (0600. 1200.CAT = computerized axial tomography CBC = complete blod count CF = cystic fibrosis CHF = congestive heart failure CNS = central nervous system CO = cardiac output COPD = chronic obstructive pulmonary disease CPK = creatinine phosphokinase CSF = cerebrospinal fluid CVA = cerebrovascular accident CVP = central venous pressure EC = enteric coated ECG = electrocardiogram EEG = electroencephalogram elix = elixir ext = extract GFR glomerulofiltration rate GT = gastrostomy h = hour hct = hematocrit hgb = hemoglobin hs = hour of sleep. 1300. 2200) qd = every day (0900) qh = every hour qid = four times a day (0900.. bedtime (2100) ID = intradermal ICP = intracranial pressure IM = intramuscular IV = intravenous IVP = intravenous push/pyelogram IVPB = intravenous piggyback KVO = keep vein open MI = myocardial infarction NG = nasogastric NJ = nasojejunal NPO = nothing by mouth NS = normal saline OD = right eye (oculus dexter) oint = ointment OTC = over the counter OS = left eye (oculus sinister) OU = both eyes (oculo utro) p = after (post) pc = after meals (post cibum) per = by pm = after noon (post meridian) po = by mouth (per os) pr = per rectal prn = whenever necessary PT = prothrombin time PTT = partial prothrombin time q = every q1h = every 1 hour q2h = every 2 hours q3h = every 3 hours q4h = every 4 hours (0900.0500) q6h = every 6 hours (2400. 2100) qod = every other day .. 1700. 1700) TO = telephone order tr = tincture ung = ointment UTI = urinary tract infection VO = verbal order VS = vital signs WBC = white blood count WNL = within normal limits Go to top Conversion Factors for Nursing Students Short list 1 cup (c) = 8 ounces (oz) 1 dram (dr) = 60 grains (gr) 1 dram (fl dr) = 60 minims 1 gallon (gal) = 4 quarts (qt) 1 glass = 8 ounces (oz) 1 grain (gr) = 64.57 milliliters (mL) 1 pint (pt) = 16 ounces (oz) 1 pound (lb) = 16 ounces (oz) 1 quart (qt) = 0.057 quarts (qt) 1 milliliter (mL) = 16.93 mL . 1300.2 pounds (lb) 1 liter (L) = 1.8 milligrams (mg) 1 gram (g) = 15.43 grains (gr) 1 inch (in) = 2.23 minims 1 minim = 1 drop (gt) 1 ounce (oz) = 2 tablespoons (tbsp) 1 ounce (oz) = 8 drams (dr) 1 ounce (fl oz) = 29.946 liters (L) 1 quart (qt) = 2 pints (pt) 1 tablespoon (tbsp) = 3 teaspoons (tsp) 1 teacup = 6 ounces (oz) 1 teaspoon (tsp) = 4.54 centimeters (cm) 1 kilogram (kg) = 2.qs = quantity sufficient RBC = red blood count ROM = range of motion s = without sc = subcutaneous sl = sublingual sol = solution sq = subcutaneous SR = sustained release ss = one half S/S = signs and symptoms stat = immediately supp = suppository susp = suspension syr = syrup tab = tablet tid = three times a day (0900. Long list 1 cental = 45.43 grains (gr) 1 hand = 4 inches (in) 1 inch (in) = 2.57 milliliters (mL) 1 palm = 3 inches (in) 1 pennyweight (dwt) = 24 grains (gr) 1 pint (pt) = 16 ounces (oz) 1 pint (pt) = 4 gills 1 pound (lb) = 16 ounces (oz) 1 pound (lb) = 350 scruples 1 quart (qt) = 0.93 mL Go to top .000 grams (g) 1 kilogram (kg) = 2. fluid (fl oz) = 29.000 micrograms (mcg) 1 milliliter (mL) = 1 cubic centimeter (cc) 1 milliliter (mL) = 15 drops (gt) 1 milliliter (mL) = 16.2 pounds (lb) 1 liter (L) = 1000 milliliters (mL) 1 liter (L) = 1.54 centimeters (cm) 1 kilogram (kg) = 1.14 centals 1 tablespoon (tbsp) = 3 teaspoons (tsp) 1 teacup = 6 ounces (oz) 1 teaspoon (tsp) = 60 drops (gtt) 1 teaspoon (tsp) = 4.359 grams (g) 1 centimeter (cm) = 10 millimeters (mm) 1 cubic centimeter (cc) = 1 milliliter (mL) 1 cup (c) = 8 ounces (oz) 1 drachm = 3.8 milligrams (mg) 1 gram (g) = 1.23 minims 1 minim = 1 drop (gt) 1 ounce (fl oz) = 2 tablespoons (tbsp) 1 ounce (oz) = 20 pennyweights (dwt) 1 ounce (oz) = 24 scruples 1 ounce (oz) = 31.1 grams (g) 1 ounce (oz) = 480 grains (gr) 1 ounce (oz) = 8 drams (dr) 1 ounce.55 milliliter (mL) 1 dram (dr) = 60 grains (gr) 1 dram (fl dr) = 60 minims 1 gallon (gal) = 4 quarts (qt) 1 gill = 4 ounces (oz) 1 glass = 8 ounces (oz) 1 grain (gr) = 64.000.057 quarts (qt) 1 meter (m) = 1.000 milligrams (mg) 1 gram (g) = 1.000 micrograms (mcg) 1 gram (g) = 15.000 millimeters (mm) 1 meter (m) = 100 centimeters (cm) 1 milligram (mg) = 1.946 liters (L) 1 quart (qt) = 2 pints (pt) 1 scruple = 20 grains (gr) 1 stone = 0. First a little test of basic math: Which of the following statements are True? 1. This trick is about applied math. gallons. This is seriously useful stuff. Maybe you've learned some algebra. you too can learn "dimensional analysis. miles per second. We're talking about measurable stuff you can count or measure." First off. 1 7/8 = 15/8 4. 16/5 = 3 1/5 3. 7 1/8 x 3/4 = 5 11/32 8. xiv = 14 . 10 1/5 . Anything you measure will have a number with some sort of "unit of measure" attached. This is something you will have occasion to do in real life. however.6 3/5 = 3 3/5 7. not about numbers in the abstract. 35% = 0. 5/8 ÷ 1/16 = 10 9. let's get rid of the big words." For a fraction of the effort needed to learn algebra. 2/3 + 3/4 = 19/12 5. or pizza slices per person. A unit could be miles.35 10. but do you ever use it? Ever foresee using it? For most people the answer is "not after the final exam. 5/9 + 2/3 = 1 2/9 6.Appendix A Fun with Dimensional Analysis Dimensional analysis (also known as the factor-label method) is by far the most useful math trick you'll ever learn. peas per pod. 20/48 = 5/12 2. What this is all about is just conversion-converting one thing to another. so rephrase "seconds in a day" to "seconds per day. Ask yourself. click Med-math Practice problems) 1. If you missed any. review: 1. what you want to know is: . If you're up to speed in DA. "What units of measure do I want to know or have in the answer?" In this problem you want to know "seconds in a day. How many seconds are in a day? Okay. that's fine because you're not going to solve THE problem. translate the English into Math. Math is a sort of shorthand language for writing about numbers of things. it works fine. Finding a common denominator 5. Multiplication of fractions 8. so this is not a med-math problem. don't panic. Subtraction of fractions 7. Reducing to lowest terms 2. If you have no idea what the answer is or how to come up with an answer. but as an introduction to dimensional analysis (DA). what do you do? First. skip this answer. which should be 17/12." then that's a step in the right direction. Changing an improper fraction to a mixed number 3. Addition of fractions 6. as with all DA problems. What you are going to do is break the problem down into several small problems that you can solve." In math terms." After you figure out what units you want to know. and here's how. If you can rephrase what you want to know using the word "per. a.All are true except #4. Percent 10. Roman numerals (Click back button to go back to test if you are taking it) Go to top 25 Examples (To take as a test first. Changing a mixed number to an improper fraction 4. Division of fractions 9. Otherwise. are true or equivalent (60 seconds = 1 minute). You know that there are 24 hours in a day (and in one day there are 24 hours). so. All you need to do now is pick from these statements the ones that you actually need for this problem. the minutes will cancel out. Ask. then you know enough to solve the problem--but first translate what you know into math terms that you can use when solving the problem. You start with "seconds" on top. The problem is you have "minutes" on the bottom but you want "days. of course. so forget about the seconds--they're okay..." You need to get rid of the minutes. "From all the factors I know. "What do I know?" What do you know about how "seconds" or "days" relate to other units of time measure? You know that there are 60 seconds in a minute. what do I need to know?" Remember that you want to know: So pick from the things you know a factor that has seconds on top or day(s) on the bottom. You could pick either of the following two factors as your "starting factor:" Write down your starting factor (say you pick 60 seconds per 1 minute): Now the trick is to pick from the other things you know another factor that will cancel out the unit you don't want. With minutes on top and bottom. or conversion factors. Ask. The connection you need. write it out: All of these statements. You want "seconds" on top in your answer.b. If in doubt. You cancel minutes out by picking a factor that has minutes on top. is that there are 60 minutes in an hour (and in one hour there are 60 minutes). You also know that in 1 minute there are 60 seconds. If you could now connect "hours" and "minutes" together you would have a sort of bridge that would connect "seconds" to "days" (seconds to minutes to hours to days). c. When you have this kind of connection between units. These are two ways of saying the same thing. So you need to pick 60 minutes per 1 hour as the next factor because it has minutes on top: .. and divide by all the bottom numbers. so you need to pick a factor that cancels out hours: d. but you want seconds per day. Only then do you need to worry about doing the arithmetic. which might cause you to doubt if you will be giving the ordered dose. If you set up the bridge so the units work out.8 mg = 324 mg. Plug in conversion factors that cancel out the units you don't want until you end up with the units you do want. Solve it. you WILL get the right answer every time. In this case you just need to multiple 60x60x24 to get the answer: There are 86. gives 300 mg as your answer. then. 1 gr Rounding to 60 mg/1 gr. How many milligrams is the order for? To get from grains to milligrams you'll need a conversion factor like 1 gr = 64. unless you push the wrong button on your calculator.You now have seconds per hour. so you decide that's close enough and give 1 tab. 5 gr x 64.8 mg. . as is often done. When you have cancelled out the units you don't want and are left only with the units you do want. You are to give "gr 5 FeSO4" but the available bottle gives only the milligrams of iron sulfate per tablet (325 mg/tab). Here's how this problem might look if it were written on a chalkboard: Remember that you don't need to worry about the actual numbers until the very end. then you know it's time to multiply all the top numbers together.400 seconds in a day. 2. Just focus on the units. since the minutes have cancelled out. 4. They ask you how long the bottle will last. You are shadowing a nurse during a clinical who receives an order to adjust the infusion rate of a pump so that 1. STAT. so rounding to 5 mL is reasonable. How much should you draw up into which syringe? Your answer will be in mL (cc). you could start with 1 mL/50 mg: 1 50 mg mL x 35 mg = 0. Your set up: 35 mg mep. at least be thinking "mL of what?" "mg of what?" 6. You realize you will give less than 1 mL. but you figure "days" is the better choice for an answer unit.6 mg of lidocaine are being delivered per minute. x 50 mg mep. On hand are 1 cc and 3 cc syringes. Your order is for meperidine (Demerol) 35 mg.7 mL If you don't actually write down full labels. 5. IM.5 days. so you tell them the bottle will last 12 days. You give your home health patient an unopened 500 mL bottle of guaifenesin and tell them to take 2 teaspoons 4 times a day as ordered. Hanging is a 100 cc .3. You just opened a 500 mL bottle of guaifenesin and will be giving 1 tablespoon per dose. since you know that you want "mL on top" in your answer. sol = 0. You could give an answer in hours or weeks.93 mL 3 tsp 1 tsp x 1 tbs = 33 tbs Rounding to 5 mL gives you the same answer. 1 mL mep. You know from the label that there is 50 mg meperidine in 1 mL of meperidine solution. sol or. How many doses are in the bottle? In other words how many tablespoons are in 500 mL? 500 mL x 4.7 mL mep. the number of milliliters that will contain 35 mg meperidine. Your set up: 500 mL x 1 5 mL 2 tsp tsp x 4 doses 1 dose x 1 day = 12. Available is a 2 mL vial containing 50 mg/mL meperidine. so start with mL on top: 100 mL MS sol x 2. sol Checking to make sure all the units of measure. but admits that at the moment her brain doesn't seem to be working. He is receiving 60 mL Jevity per hour as ordered when the pump fails and no other pumps are available.0 mg MS 5 min 0. Your answer will be in drops/min. The reason is drop size varies from 10 to 60 drops per mL.4 grams lidocaine.piggyback containing 0. How would you set up and explain the problem to her? We want to know mL/hr. but don't see it.4% solution. It occurs to you that you could reset the pump to deliver 0. Your hospice patient is on a double pump.2 mL IV push. then go back to 5 mL/hr. You decide to adjust the drip rate accurately to give the ordered amount. so: 60 1 hr mL 1 mL x 12 60 min drops min x 1 hr = 12 drops or 3 drops every 15 seconds which is easier to count.0 mL L. On your first day of clinicals at a long-term care facility you are caring for a resident receiving total enteral feeding through a PEG tube. His over-extended regular nurse hangs drip tubing. sol = 24.2 mg MS in 5 minutes. You finally find the tubing used and the package says 12 drops/mL. the nurse tries to solve the problem on a calculator. She assures you she can always do problems like this on tests. We now just have to change minutes to hours. now is the time for the calculator. x 100 hr mL L. x 60 min 1 hr 400 mg L. and it is the drop factor (drops/mL) that you need to know. and the other has a 100 cc bag containing 2 mg morphine sulfate (MS) running at 5 cc/hr for pain management. 8.0 each time.6 mg/min should work. we can now set the pump with confidence.2 mg 1 hr MS x hr 60 min = 120 mL MS sol . 1. You recall seeing tubing in the supply room and go there looking for the same tubing as what was hung. and get from mg to mL. Without writing anything down. then x x ÷ x ÷ ) and getting 24. You would normally use a prefilled syringe containing 1 mg/1 mL MS and give 0. 7.6 mg 1 min L. except for mL and hr. At what rate should you set the pump? Again you want mL/hr. She begins to show signs of breakthrough pain and her doctor orders 0. Crunching the numbers twice (first x x x ÷ ÷ . It turns out that "about right" was about twice the ordered rate. adjusts the drip rate to something that "looks about right. which has "time" on the bottom so starting with 1. One side is running NS at 30 cc/hr KVO. a 0. After the fifth different and incorrect answer you find a piece of scratch paper and offer to show her how to set up the problem. cancel out.2 mg MS STAT. but on looking in the narcotic cabinet you find none available and the pharmacy is closed." and rushes on to her next demand. What do you need to know to do so? You look in the trash for the tubing package. The manufacture would have calibrated their drip chamber and put the number of drops/mL on the package. 3 g x 1 5 mL mL x 1 tsp = 0.8 g/cc. What questionable assumption does the textbook make? While 1 tsp = 5 mL is a valid conversion factor. KCl is 1.2). and 1/2 tsp baking soda. 2.0. In powdered form they would weigh less.2 tsp (close to 1/4 tsp) Baking soda: 2. As a home health nurse you need to help a client make homemade pediatric electrolyte solution using the following recipe: 1 L boiled water. 10. 2. and until you look up the densities and factor them in you wouldn't know if it matters or not. remains at 1/2 tsp.5 g lite salt (KCl). The answer. 1.63 tsp (closer to 2/3 than 1/2) 0. The density of granulated sugar is 0.7 g/cc.5 g baking soda. 1/4 tsp salt. you need the volume to be infused: 100 mL 2. In another textbook you are given the following example: Order: Chloromycetin 300 mg 1V bolus via saline lock. is 1 qt boiled water. 2 tbsp sugar.Now that you know the rate.0 g/cc.3 g/cc) would weigh 6.5 g x 1 mL x 1 tsp = 0.25 g 1. Does taking the density into account really matter? Realizing that density is something to take into account matters.9 tbsp (not 2. 30 g sugar. so a teaspoon of each would actually weigh between 3.7 g 1 cc 5 mL 3 tsp Salt: 1. and baking soda is 0. how many minutes will it take for the pump to deliver 10 mL at 120 mL/hr? 60 1 hr min 120 mL x 1 hr x 10 mL = 5 min 9.0 mg MS MS sol x 0. A teaspoon of salt (density 1. To do the conversions right. Since water has a density of 1 (1 g/1 cc). The density of salt. so a teaspoon would weight over twice as much. with density 1.6. factor in the density: Sugar: 30 g x 1 cc x 1 mL x 1 tsp x 1 tbsp = 2. Directions: Reconstitute with 10 mL sterile .5 grams. Label: Chloromycetin 1 g. 1 tsp = 5 g is valid only when measuring water. NaHCO3 2. these densities are for the solid substances. "Teaspoon" is a measure of fluid volume and not weight.5 g/cc and 6. KCl 2. A textbook on clinical calculations includes the following conversion for household to metric: 1 teaspoon = 5 mL = 5 g. right? But wait. Since only kitchen measuring cups and spoons are available you need to convert from metric.0 tbsp) 0. according to the textbook.2 mg MS = 10 mL MS sol Just to double check.5 g salt. is 2.5 g/cc.2 g/cc (sugar 1. 1/2 tsp lite salt.8 g 5 mL KCl. however. 1 tsp of water would weigh 5 grams. Assuming 5 g/tsp for each seems a bit rough. " which is quite an unnecessary bit of information for solving this problem." You can't use "mL water" and end up with "mL Chlor. sol 11. how would you prepare 1 L (or so) of normal saline (0. x 1 100 mg Chlor. What error did the textbook make? The set up is in error due to a failure to fully label units. what you want to know." You have to ask. so 0. In a home setting.9% NaCl) using water and table salt if you have only a measuring cup and a teaspoon? On hand is an unopened 1 lb box of salt.1 cups water x 1 cup = 1/4 cup bleach 12. pick a factor that has "mL Chlor. 10 mL water = 3 mL water (not!) The correct set up should be: 300 mg Chlor. the set up is not. 1 g Chlor. solution. is "mL Chloromycetin sol" and not just "mL. The key is to clearly understand what 0. If you knew the density of granulated salt you could convert from a desired weight of salt to a volume of salt." When you add 10 mL water to reconstitute you will end up with somewhat more than 10 mL Chlor. How may mL of Chloromycetin should be administered? Equivalents: 1 g = 10 mL. 2 L sol x 1000 mL x 3 mL bleach x 1 oz 1L 100 mL sol 30 mL 8 oz But how much water? The solution is 97% water.water for injection to yield 100 mg/mL.9 parts salt by weight to 100 parts salt solution (not water) by weight. 300 mg Chlor. though the text incorrectly uses it. The 10 mL is "10 mL sterile water. x 1000 mg Chlor. 1000 mg = 1 g 300 mg x 1000 mg 1 g 1 g x 10 mL = 3 mL While the answer "3" happens to be right. sol" in your answer. sol. "10 mL of what?" Your answer unit. sol" and "10 mL/g" should be "10 mL water/1 g Chlor. sol = 3 mL Chlor.9% means. sol" in it and in the right place. Since you want "mL Chlor./mL Chlor. x 1 g Chlor.9% means 0. Since you can only measure volume (using cup and tsp). you will somehow have to determine the density . right? 2 L sol x 1000 mL x 97 mL water x 1 oz 1L 100 mL sol 30 mL 8 oz x 1 cup = 8. You are given "100 mg/mL" which should be more completely written as "100 mg Chlor. mL Chlor. How would you prepare 2 L of 3% sodium hypochlorite (bleach) and water solution? You have only a measuring cup. Salt is measured by weight. How would you adjust the drip rate? First. The two are compatible so you plan to draw up both in the same syringe. The order is for meperidine 60 mg and atropine gr 1/150. and what will the drip rate be? You want to know mg of Tagamet. IM. Tagamet is ordered 200 mg.of salt. . You have an order to infuse 1000 mL of D5W (5% Dextrose in water) IV over a period of 5 hr. The drip rate would be: x 2 100 mL NS mL T. Since you want gtt on top and 10 gtt/mL has gtt in the right place. 100 mL NS 300 mg T. your answer unit. What you want to know is the number of teaspoons per quart. How much of each will you draw up? For both you want to know mL.8 1 gr 0. 60 1 150 mg 100 mg x 1 mg mL x 1 = mL 0. what do you want to know? The flow rate in gtt/min.3 mL T. so divide by 3 and count for 20 seconds.3 fl oz or 1. but the tubing set package notes that the drop factor is 10 gtt/mL. Available is Tagamet 300 mg in a 2 mL vial of aqueous solution. You could look up the density. The meperidine on hand is 100 mg/mL and the atropine is 0.3 fl oz salt x 0.1 mL meperidine atropine gr x 64.3 oz/fl oz. which are the answer units. No pump is available. q6h.6 = mL 1.4 mg 15.4 mg/mL. How much Tagamet will you inject into the Buretrol. Recalling that density is weight/volume. sol = 1. 10 gtt/mL makes a perfectly good starting factor--from there you just need to get from mL to min. What do you know? You're given that there are 10 gtt/mL and that the infusion rate is 1000 mL/5 hr. You are to dilute a portion of this in 100 mL NS and infuse over 20 minutes using a Buretrol with a drop factor of 60 gtt/mL. IV.9 oz salt 16 oz salt 100 oz salt sol 1 qt x 32 oz x 2 tbsp x 3 tsp = 1 1/3 tsp salt 1 fl oz 1 tbsp qt salt sol To make one quart you would first put the salt into a measuring cup then fill to the 1 quart mark. and gtt/min. you figure the density of salt at 16 oz/12. The set up then: 10 1 mL gtt 5 hr x 1000 60 min min mL x 1 hr = 33 gtt You wouldn't want to count a full minute. or what if you poured the box of salt (16 oz) into your measuring cup? Doing so you find that you have a bit over 12 fluid ounces of salt. 13. 200 mg T. 14. The set up follows: 12. What dose should be given? You want to know mL/dose. Half of one quarter is one eighth. sol Can you count 5 gtt/sec? Not likely. How can you do that? Consider dividing 1/4 by 2. sol 16.5 mg kg x day 4 doses x 1 day dose x 25 kg = 12. How much heparin has been given? You want to know Units/mL. start with: 5 mL x 5 mg 12.5 mg/kg/day--a safe dose.3 min mL T. What you know is that you will give 60 mg per 13 lb body weight per dose or 60 mg/13 lb/dose. which is equal to ft/(sec x sec) or ft/sec2. so nothing tricky here: . Whenever you have x per y per z.2 lb x 3 dose = 30. A child with severe poison ivy weighs 25 kg and Benadryl po 5 mg/kg/day is ordered q6h. Acceleration. which true but is unusable in this form. Since you want mL on top. sol = 304 gtt T. 17. so what do you do? What if you added a secondary set with a drop factor of 12 gtt/mL? 12 1 mL gtt x 20 min 101. The order is for amoxicillin 60 mg.5 mg/5 mL solution. po. You are to infuse heparin 5000 U in 250 mL NS at 30 mL/hr. is measured in feet per second per second or ft/sec/sec. so you rewrite it as 60 mg/13 lb x 1 dose. sol = 60 gtt T.5 mL 18.3 mL min T. tid for a child weighing 13 lb. The pediatric dosage range is 20-40 mg/kg/day in three equal doses. Is the dose safe? You want to know mg/kg/day for this child.60 1 mL gtt x 20 min 101. 60 mg x 2. rearrange in the form x/y*z and everything will stay straight. Benadryl is available as a 12. to give another example.5 mg 13 lb x 1 dose 1 kg 1 day kg x day = 30. but how to figure that: 1 4 2 = 4 1 2 x 1 4 = x 1 2 = 1 8 Dividing by 2 is the same as inverting 2 to get 1/2 and multiplying. What is the concentration of heparin solution? When you clear the pump you note that 187 mL have been infused. so this should work as a starting factor: 10 mcg x 60 min x 1 mg kg x min 1 hr 1000 mcg 2. Nipride is ordered and you are to titrate to maintain the systolic blood pressure at 150 mm Hg. and you are ordered to infuse 250 mg dobutamine in 500 mL NS at 10 mcg/kg/min.29 m2.29 m2 = 17. Available is Nipride 50 mg/250 mL. so you could start with 1 day/3 doses or 180 mg/m2/day: 1 day x 3 doses m2 x day 180 mg dose x 0. which has time on the bottom. The piggyback contains 120 mg Lidocaine in 100 mL NS.5 mL 2. The range is 3-6 mcg/kg/min. Your patient weighs 135 lb. After converting to 10 mcg/kg x min you note that time is also on the bottom. so relax and focus on what you want to know. At what rate will you set the pump? You want to know mL/hr. Phenobarbital 180 mg/m2/24 hours given every eight hours is ordered for a child whose BSA (body surface area) is 0.800 U/mL U 19. How much will each dose be? You want to know mg/dose. Your patient weighs 143 lb. not more difficult.2 lb kg x min 1000 mcg 120 mg 1 hr hr 22. You are to give Lidocaine 30 mcg/kg/min to a child weighing 55 lb. How many milligrams of dobutamine will infuse per hour? You want to know mg/hr.4 mg 21. Starting with the patient's weight usually works out: 55 lb x 1 kg x 30 mcg x 1 mg x 100 mL x 60 min = 37. • What is the concentration of the solution in mcg/mL? Here you want mcg/mL. so: 50 250 mL mg 1 mg x 1000 mcg = 200 mcg/mL .2 lb x 1 kg hr x 143 lb = 39 mg 20. Titration problems are just longer. A microdrip chamber (60 gtt/mL) is used with a pump.5000 250 mL 187 mL mL sol U sol x = 20 U 20 = 74. or again just double 55 to get 110 mL/hr for the upper range. How would you prepare 500 mL of a 1:35 bleach solution from a 1:10 bleach solution using water? . could be administered? 1 kg x min 135 lb = 184 mcg low range 3 mcg x kg x min 2. just multiple by 2 to get 368 mcg/min. • What is the titration factor in mcg/gtt for the low range? Don't know what a titration factor is? It don't matter 'cause you know you want mcg/gtt: 184 1 min • mcg 55 gtt x gtt 1 min = 3. how many mcg/min will the patient be receiving? You want mcg/min and from the above. If you increase the gtt/min by 5 gtt. which is also 55 gtt/min: 55 mL x 1 hr 60 min 1 mL 1 hr min x 60 gtt = 55 gtt You could plug in 368 for 184 and recalculate.• How many mcg/min. • Within what range will the pump rate be set? What's the low and high rate the pump could be set at in mL/hr? 184 mcg x 60 min x 1 min 1 hr 200 mcg hr 1 mL = 55 mL low range. How many mcg/min is the patient now receiving? You again want mcg/min and are going from 60 to 54 gtt/min: 3.2 lb Since the high range is twice the low.3 1 gtt • mcg 1 min x min 60 gtt = 198 mcg After 1 hr. going from 55 to 60 gtt/min: 3. the systolic blood pressure is 120 mm Hg.3 1 gtt mcg 1 min x min 54 gtt = 178 mcg 23. so you decrease the gtt/min by 6 gtt.3 mcg The patient's systolic BP is currently 170 mm Hg while receiving the low range dose. lower and upper range. b. . 3. Setup: What factor should you start with? Since you know that the patient's weight is a determining factor. 3. but the point is you don't even have to know what the units are. but you decide to pick 79 kg as your starting factor. so 60 min/1 hr would be a logical starting factor (you would then just have to get from "min" to "mL").9 milliscruples of Morphine IV for each stone of body weight to be administered over a 300-minute period. 10 mL 1 mL b. you should avoid confusion.You want to know how much concentrated bleach solution (mL c. and that you are to infuse 0. 24. To the 143 mL of concentrated bleach solution you would add enough water to make 500 mL 1:35 solution. (or in math terms you know 60 min/1 hr.) you need to make the weaker solution (mL w. and 1 hr/60 min).14 centals per stone. The rest of what you need to know will have to be looked up.55 mL/drachm would also be a logical starting factor. And everyone knows that in 1 hour there are 60 minutes and in 60 min. and 3. b. Kissoff. Is the ordered dose safe? (Yes. then use the Back button on your browser to return. You are also told that there are 0. orders 1.b. you could start with it. wishing to test your perspicacity. x 500 mL w.0019 scruples per stone per 300 minutes (it helps to rephrase the problem using the word "per").b.). You also know that since you need "hours" in your answer you will need to get from minutes (300 minutes) to hours at some point.4 pennyweights of Morphine dissolved in 1000 drachms of solution. since you want "mL" on top. 20 grains per scruple. you realize you get the same answer no matter what order you multiply (or divide) your terms in. = 143 mL c. At what rate should you set the pump? Your drug guide says that 0. 24 grains per pennyweight. which forces you to lookup "cental" where you find that there are 45.55 milliliters per drachm. so your answer will have to be in these units of measure. Available is 1 gill of Morphine (MS) solution having a concentration of 0. Or.4 pennyweights MS per 1000 drachms and that you have a whole gill of this solution however much a gill is. What do you know? From the problem you know the patient weighs 79 kg. If you fully label all amounts.8 to 10 mg of morphine can be given per hour. x 1 35 mL w. just how to get from what you are given to what you want to know.36 kilograms per cental.b. all the units of measure are real. start by asking what do you want to know? If you've worked with IV pumps you know they are programmed in mL/hr. there is 1 hr. Or. If you recall the Commutative Law of Multiplication. c. you know "hours" has to be on the bottom.) Breaking the problem down stepwise: As always. Looking up "stone" you find that there are 0. Doing so you find that there are 4 ounces per gill. See the long list of Conversion factors for clues. mL b. The patient weighs 79 kilograms.b. if seldom used. Dr. since you know your answer has to be in mL/hr. 14 centals 1 stone x 300 min 1 hr 1 scruple 24 grains 0. but fortunately your grandmother has a sure cure.36 kg 0. She gives you an eyedropper bottle labeled: Take 1 drop per 15 lb of body weight per dose four times a day until the geebies are gone. your answer unit.55 mL = ? mL 45.0019 scruples x 60 min x 20 grains x 1 pennyweight x 1000 drachms x 3. but is the dose safe? Go back to step 1: you'll need to know mg/hr. what do you want to know? You want to know how long the bottle will last. Do you need to see her before leaving to get a refill? Now this one is a bit hard if you haven't been paying close attention. So you write down "Answer units = days/bottle" What do you know to start off with that you might need to know? You write down the following: .4 pennyweights x 24 grains 1 hr 3. and since you have 1 gill (4 ounces) or about 120 mL of morphine solution. 60 drops=1 tsp. and you'll need a conversion factor to get from grains to milligrams. Since you need "hr" on the bottom. punch the numbers in (correctly) and you got it: 35 mL/hr. You have come down with a bad case of the geebies. You could figure out days/bottle or weeks/bottle and see if the bottle will last longer than 3 weeks or 21 days. but on the high side. First. 25.8 mg = 6. You test the eyedropper and find there are actually 64 drops in a teaspoon. so you'll be monitoring your patient closely. You weigh 128 lb. 35 mL x 1 drachm x 0. Contains gr 8 heebie bark per dr 100 solvent. and the 4-oz bottle is half-full.55 mL 1000 drachms 1 pennyweight 1 grain x 64. are you going to have enough? Go figure. start with 35 mL/hr.4 pennywts 1 drachm hr Does everything cancel out except for "hr" and "mL"? Bingo.79 kg x 1 cental x 1 stone x 0.1 mg hr The dose is safe. Does the answer make sense? The flow rate is within usual limits. You are going on a three-week trip and are deeply concerned that you might run out of granny's geebie tonic. Oh. You figured out how much of the bottle you would use in one day. . At this point you realize that when you calculated 22. you can't take 8. you were not figuring on 9 drops/dose. Concluding that you have enough. You set the problem up: Houston.533 drops per dose. or start over with 128 lb on the bottom. so you figure it out: As a practical matter. What should you use as a starting factor? You pick 128 lb because it's something you're given and starting with weight usually works. then there is 2 oz of tonic in it. this time picking a starting factor that already has "day" or "bottle" in the right place. You decide to start over. and having enough may not be the same thing. but you could figure it out dimensionally if you wanted to: You would then end up with "days/half-bottle" in your answer. or put it in the middle somewhere. What to do? You could hit the 1/x button on your calculator if it had one. or invert the answer by dividing 1 by 0.044. You note a small difference. At some point you need to know how many drops per dose you will need to take. So. it looks like you'll have enough. The story continues: You leave on your trip and on the 19th day you run out of geebie juice. however. You could even put 128 lb on the end and on the bottom. You ended up with units reversed from what you wanted.You realize that if a 4-oz bottle is half-full. but it's easier to just go with 2 oz/bottle. but conclude that you have just enough geebie tonic. What? Can you do that? Sure you can. we have a problem. you have to round off. You sit in a stunned stupor trying to figure out where you went wrong in your calculations. You didn't spill any.5 days/bottle. and no one took any. You decide to recalculate to see if rounding up to 9 makes a significant difference. rephrasing parts of it.You finally realize there might not have been 2. You now need to pick a starting factor. everything you know that relates to the problem. more or less. was that you had 2 + 0. Figure out what answer unit(s) you want to end up with. . Determine the starting factor and answer unit. Recalculating using the low and high values. 2. Do the math and solve it. Write down. in math terms. 4th ed. Plug in conversion factors that allow you to cancel out any units you don't want until you are left with only the units you do want (your answer units). You may need to read the problem several times. but what you were given. Break THE PROBLEM down into small ones you CAN solve. recheck everything. Go to top Appendix B Go to top A Critique of Clinical Calculations: A unified approach. and would have gone to see Granny for a refill. There could be anything from 1. The steps for doing dimensional analysis are given in the textbook as: 1. pick a different starting factor and start over. so you can translate everything into math terms. You may need to look up a few conversion factors. If you had figured out the correct answer of 21 + 5 days the first time.0 oz of tonic in the bottle to begin with. you find you had enough tonic to last somewhere between 16 and 26 days. Now double-check your calculations. you would have realized you had only slightly less than a 50/50 chance of running out. This is usually easy. If you can't solve the problem. If possible pick one that already has one of the units you want in the right place.0 + 0. not difficult.5 oz in the bottle.5 oz of tonic.5 to 2. Ask yourself if the answer seems right or reasonable. You wish you had measured the amount and found that the bottle contained 2. Otherwise start with something you are given that is not a conversion factor. Go to top Summary • • • • • • • • Don't panic.05 oz of tonic. A measurement like "half a bottle" should not inspire great certainty. Formulate a conversion equation. If not. but that's inconvenient. If the answer unit is always given in the examples used. Equating 1 grain with 60 milligrams when the actual equivalency is closer to 64. It is oddly inconsistent to insist on carrying out calculations to two decimals. rounding to the nearest tenth. When. This skill is not emphasized in the textbook. properly labeled factors they can later use to solve the problem. Ignoring a given unit. Determining the answer unit or units is crucial. It is possible to solve a problem and come up with answers that differ by as much as 10% depending on which approximate conversion factors you decide to use. then this is because the examples have been contrived to be more simple and consistent than actual problems tend to be. after the answer unit is determined. 49) gives 25 mg/kg/24 hr. yet this is what the textbook does. In this form it can be used." Indeed. It is preferable. The problem (p. not per dose. or "mL/day. which to use." Omitting the "per day" part doesn't alter the fact that that is what you want to know--not per hour. and you end up with the desired answer with the right units attached: . is questionable. a problem involving amount/body weigh/day comes up. the solution is presented in an unorthodox way. as an aside. all undesired units cancel. they are not always obvious and can be challenging to determine. but per day. All examples used throughout the text use only numbers having a single unit attached for starting factors. in such cases. or 1 mL to 15 minims (actually 1 mL = 16. When doing dimensional analysis it is essential that all the units given should be used and accounted for. to determine everything you know that might be relevant to solving the problem. then pulling it out of thin air at the end is poor technique. as is equating liters and quarts. While many conversion factors are approximations. it is not written as ft/sec/sec. but "250 mL/hour" is not.3. initially. and fraction of a percent errors are unimportant in medication math. then decide. So if you're given mg/kg/day. when acceleration is measured in feet per second per second. the preferred way to deal with such a "triple decker" is to rewrite it as mg/kg x day. reading the problem correctly is the only challenge. There is actually a simple rule that applies here. which of the factors you know would make an appropriate starting factor.23 minims). In some real-world problems no starting factor is given. For example. then. For some problems. Students need to be able to translate sometimes convoluted English descriptions of a problem into clear. If + 5% errors are acceptable. some problems cannot be solved if they have a single unit starting factor (see example 3 in Appendix A). but as ft/sec2 because ft/sec/sec is equal to ft/sec x sec. when far greater errors can be introduced by using loose approximations. Apparently "1 hour" is an acceptable starting unit. Solve the conversion equation. The solution is given as: The problem is that the correct answer units should be how many mL should be administered per day. or several possible starting factors are given with no way to decide. in chapter 6. any answer to a test question that is within 5% of the correct answer should be counted as correct. 10 percent errors are a bit worrisome. This is not correct as starting factors are often in the form of "something per something.8 mg. " then divide by 4 to get "mL/dose. A student might try to logically extend this technique to determine mL/hr: The student who notices that the answer doesn't make sense might wonder what went wrong." Problems of this sort are common. an example is shown. at least. and are shown conversion equations like the following: . The textbook method is to calculate "mL. this problem would become more difficult to solve. however. as a model for students to follow. page 184. Would they realize that when "mcg" was cancelled that "3 1/min" was left requiring the use of 60 min/1 hr instead of 1 hr/60 min? Trying to explain how to work around the poor technique employed by this example only digs a deeper hole. to determine how many mcg/min must be administered to a 215 lb patient at 3 mcg/kg/min: In this example. thus greatly increasing the risk of administering an overdosage (sic). The better response to student confusion would be to have them put a big X mark over this section of the textbook and show them a sensible way to set it up: Another case of flawed technique arises in Chapter 10. minutes are not omitted then added at the end. The risk of confusing some students by introducing a new rule can hardly be worth the risk of error introduced by teaching a flawed technique.If the problem called for "mL/dose" given 4 doses per day. but merely confusing to many students and visually awkward. and the technique is not even erroneous. Students are given problems that require converting from mL/hr to gtt/min. In Chapter 10. As the text acknowledges. and it is unfortunate that the authors neglect to show students how to logically deal with them." Students must remember to perform this final "critically important" step which would not exist if better technique were used. "it is easy to forget to divide the total daily dose into the prescribed number of doses. then the solution is straightforward: If "day" were omitted. 1. 10 gtt = 1 mL. . One is procedural--there is no logical way to pick a starting factor as the first step. you would be committing mathematical suicide as the problem would be rendered unsolvable once "hour" is cancelled out. Students should be told to just ignore the nonsensical "1 min" and "1 hour" starting factors.The problem." The initial starting factor of "1 min" is spurious. I can meaningfully say that I know there are 10 drops per mL. If you were to introduce "1 hour" as a starting factor in example 3 in Appendix A. As mentioned.3 = 33 gtt Flow Rate: 33 gtt/min For review. The other is that "1 min" is a meaningless factor. It is not a given. and it means absolutely nothing to say that you know "1 min" or "1 hour" or "1 cabbage. let's go over this problem. the problems are perfectly setup to yield the correct answers with the correct answer units. is that the correct answer unit is "gtt/min" and not "gtt" as it appears. The correct answer is just pulled out of nowhere and declared to be "33 gtt/min. there is no such requirement when doing dimension analysis. Here's an actual example from chapter 10: Calculation of IV Flow Rate When Total Infusion Time is Specified Order: 1000 mL of D5W (5% Dextrose in water) IV to infuse over a period of 5 hr Drop Factor: 10 gtt/mL Starting Factor Answer Unit 1 min gtt (drops) Equivalents: 1000 mL = 5 hr. but it means nothing to say that I know "1 min" in the context of this problem. There are two errors relating to the starting factor. It seems that the pseudo-starting factor is used to avoid having a starting factor with more than one unit attached. however." If such meaningless starting factors are simply omitted from such examples. 60 min = 1 hr Conversion Equation: 1 min x 60 min 1 hr x 1000 5 hr 1 mL mL x 10 gtt = 33. In the above example "90 mL/1 hr" would make a logical and perfectly good starting factor. again. As to what the authors might be thinking. But through some sort of mental slight-of-mind. as in all dimensional analysis conversions. which yields 33 gtt for an answer. It should read "something per something" and not "something equals something" which leads to absurd statements like "25 mg = 1 kg" 4. 3. The answer unit is wrong. My set up then: 10 gtt 1 mL 5 hr x 1000 60 min mL min x 1 hr = 33 gtt Just omitting the "1 min" from the textbook's setup would also work. Just "gtt" doesn't cut it. therefore. one minute becomes the labeled value that must be converted to an equivalent value: number of drops. but it is logically disconnected from everything that precedes it. form an equivalent relationship. The final statement. but the answer unit is not. The number is correct. By introducing a spurious starting factor the setup is in error. not just gtt (drops). Factors are expressed as equalities. One minute. I want to know a rate of flow in drops per some unit of time. as is the resultant answer. Is there a better way to do this problem? First ask. let's see. which makes the setup wrong. 10 gtt/mL makes a perfectly good starting factor--I just need to get from mL to min. the only clue to their reasoning was given in the following paragraph that preceded this example: "In calculating the flow rate for drops per minute. is the starting factor and drops is the answer unit and these. then introduces a spurious starting factor. which they simply declare to be 33 gtt/min. What do I know? I'm given that there are 10 gtt/mL and that the infusion rate is 1000 mL/5 hr. Since I want gtt on top and 10 gtt/mL has gtt in the right place." On page 9 is the following table: Table 1-2 Conversion Equation . which is also wrong. what do I want to know? The flow rate in gtt/min.2. they finally come up with the correct answer. 5. that the flow rate is 33 gtt/min. the text manages to state an incorrect answer unit. which is my answer unit. So. is the only part of the example that is correct. 54 cm/1 inch = 25. but otherwise there is no necessary "equivalent relationship" implied.2 lb = 1 kg). which can be said to be equivalent to your answer (10 inches x 2. which appears to be what has happened.4 cm). it doesn't matter what order the factors on the left side are multiplied in. although usually only one or two factors qualify to be thought of as logical starting factors. One could speak of an equivalent relationship between the "numerator" and "denominator" of a conversion factor (2. but such problems should not be taken as a model for all DA problems. and thus be the starting factor.2 lb/1 kg means 2. and it forms a special "equivalent relationship" with the answer unit.This table reveals how the authors think about dimensional analysis. those who do must do so in spite of the textbook and not because of it. it has only one unit associated with it. I don't think it is going too far to suggest that the poor technique exhibited by the textbook makes it difficult for students to master med-math. the simple conversion problem. It appears that such fundamental misunderstandings underlie the errors in the textbook. Problems that do not conform to their notions are tortured into compliance by introducing spurious starting factors and using obviously incorrect answer units. In this subtype of problem you have only one logical starting factor. Indeed. Both starting factors and answer units are often in the form of something per something. without any equivalence between starting factor and answer unit. They see the starting factor as something given. There is a particular type of DA problem. You could start with miles/hour and end up with seconds in your answer. there can be only one starting factor. that does involve going from one unit of measure to another equivalent measure (such as converting from feet to meters). In between are conversion factors that are fundamentally different from the starting factor. Therefore any factor could be first. for example. Go to top Recommended Corrections to . The only equivalent relationship is between what is on the left side of the equal sign and what is on the right side. which. must also have only a single unit associated with it. being equivalent. By the Commutative Law of Multiplication. All of these assumptions are incorrect as generalizations about dimensional analysis. then the answer unit can have only one unit of measure associated with it and vice versa. All the various ad hoc attempts to get around these problems result in endless trouble in the long run." whereas the correct answer unit is "mL/day. Likewise "unit conversion" is not a synonym for DA. Picking a starting factor from what you are given or know is the first step of Step III--setting up/solving the conversion equation. if the value of an equivalent can be 5% off." The belief that this is true leads to serious error and confusion in Chapter 10." The problem should be setup as: Whatever initial difficulty this technique may present for students not already familiar with it. In some (unlikely) cases answers could be as much as 10% off when several approximate equivalents are used to compound the error. the collorilary would be that if the starting factor has one unit of measure associated with it. "Step I: Determining the Answer Unit. Also. If true. Give the actual equivalents--some students will want to know. I would expect the authors to use the same terminology as everyone else by the 4th edition." Determining the starting factor should come after Step II. "Step I: Determining the Starting Factor and Answer Unit. but a more complete presentation of dimensional analysis should be given without closely following the material in this chapter. Page 7: Emphasize that several of the equivalents in the table are fairly rough approximations. In this example the answer unit is given as "mL. Some of the techniques . Page 1: A Google search shows that only this textbook and a few nursing sites associate "label factor" with dimensional analysis (DA). since the starting factor is not always given. any test answer that is within +5% of the correct value should be counted correct. The third unit given should not be dropped. Page 49: In the example at the bottom of the page you are given 25 mg/kg/24-hr (or day). there can be more than one possible starting factor. Page 2: At the bottom." While this point is nit-picky." should read. The only synonym commonly used is "factor-label method. Page 4: In the box is the statement: "When the conversion equation is solved.Clinical Calculations: A unified approach (4th ed. to be consistent. it will be seen that the starting factor and the labeled answer have formed an equivalent relationship. Triple unit factors are common and the difficulty they pose should be dealt with head on. There is a way to deal with problems of this type (25 mg/kg/day = 25 mg/kg-day) that can be consistently applied to all problems of this type. then.) Chapter 1 can be a useful supplement for students to read. and the best starting factor to use may be one of the factors determined in Step II. it is still the technique of choice and will save a lot of grief later on. The "day" is initially ignored." Page 160: Ignore examples. Omit the spurious "1 min" Starting Factors. 165. Students will get into trouble if they try to extend this example to other problems. Pages 177. you are given 50 mg/kg/day and 4 doses/day. Another ad hoc variation in technique is introduced without comment in step 1 of the first example. form an equivalent relationship. Page 159: Cross out the second paragraph: "In calculating the flow rate for drops per minute. 178: Again. Page 105: Avoid the two-step technique. and 166: Ignore these examples as above. and ignore the two examples at the bottom of the page. but not knowing what to do with "mg/kg/day" the problem is broken into two problems. and examples 2 and 3 on page 178. but not others. thus paving the way for confusion and error. The logically consistent one-step setup would be: For the second example the setup should be: In the box at the bottom on the page are several warnings ("critically important. Note that Answer Units are also wrong (should be "gtt/min. is the starting factor and drops is the answer unit and these. one minute becomes the labeled value that must be converted to an equivalent value: number of drops. 185: Ignore examples.contrived to deal with these problems work on some problems. then brought back in the second part of the problem. Also. A better setup for step 1 would be: For step 2: . In the first example. as in all dimensional analysis conversions. ignore the spurious Starting Factors and use the correct Answer Units for the last two examples on page 177. Page 50: In the two examples on this page the Answer Unit is incorrectly given as "cap" whereas "cap/dose" is what is really desired. therefore. All that needs to be done is to cross out the "1 min" at the beginning of each example and add "/min" to "gtt" (to get the correct answer unit)." "easy to forget") that do not apply when the problems are done in a single step." not just "gtt"). Pages 164. Pages 184. The technique used above has the virtue of working with all problems involving triple unit factors. One minute. what if the desired answer units were "mcg/hr?" Would students have trouble canceling out "min" with "min" apparently on top? Putting "mcg/min" on top invites confusion. Work out as above. /mL Chlor. change "mcg/min" over "kg" to "mcg" over "kg x min." You have to ask. Page 220." You are given 15 mcg/kg/dose. "How many mL should the child receive per dose?" The answer unit. You are given "100 mg/mL" which should be more completely written as "100 mg Chlor. In example 2." and "1 gtt" Page 189. solution. 221: The first example asks." When you add 10 mL water to reconstitute you will end up with somewhat more than 10 mL Chlor. the setup is in error due to a failure to fully label units. The 10 mL is "10 mL water. Page 225: Again. 3. The other 96% of the text is okay. so a one-step setup would be: That's about it. sol" in it and in the right place. should be "mL/dose" and not "mL. so solve as shown above for examples on pages 49 and 50--likewise with the second example on page 221. just omit the "1 min. pick a factor that has "mL Chlor.For steps 3 and 4.000 U/kg/day and 4 doses/day. Since you want "mL Chlor. example gives 50.. and 6. The correct setup should be: Page 205: Omit spurious Starting Factors from example." You can't use "mL water" and end up with "mL Chlor. 5. sol" in your answer. sol." Page 196: In Example a. Go to top Textbook Guide to Dimensional Analysis (as compiled from various pages throughout the textbook) Determine the starting factor* and answer unit. . therefore. though the text incorrectly uses it (and by luck gets away with it). sol" and "10 mL/g" should be "10 mL water/1 g Chlor. 190: Cross out the meaningless Starting Factors in examples 1." which is quite an unnecessary bit of information for solving this problem. "10 mL of what?" Your answer unit is "mL Chloromycetin sol" and not just "mL. 4. the answer unit. therefore. do the conversion. If it doesn't. e. Formulate a conversion equation consisting of a sequence of labeled factors. You will need enough to form a "bridge" to your answer unit(s). If a percentage is given. Reduce answer to lowest terms.g. as in all dimensional analysis conversions. as this contains the unit of the preceding numerator and facilitates cancellation of successive units. convert to decimal. it is helpful to write the denominator first. ignore the third unit. If a given is in the form mg/kg/day. One minute. and/or round off. Solve the conversion equation by use of cancellation and simple arithmetic. it is essential to determine exactly what information is sought: the known quantity called the starting factor. In setting up the conversion factors. then remember to factor the omitted unit back in. Use only conversion factors that have a 1:1 relationship It is desirable that conversion factors be arranged in a sequence so that identical units are placed diagonally. 25%. Determine conversion factors that may be needed. change to mcg/min over kg if mcg/min is the answer unit. Multiply/divide to solve the equation.Initially. Take a few seconds and ask yourself if the answer you came up with makes sense. start over. If in the form mcg/kg/min. and the desired unit to which the starting factor will be converted. is the starting factor and drops is the answer unit and these. In calculating the flow rate for drops per minute (or mL per hour) one minute (or one hour) becomes the labeled value that must be converted to an equivalent value: number of drops (or mL). it will be seen that the starting factor and the labeled answer have formed an equivalent relationship. in which successive units can be cancelled until the desired answer unit is reached. Cancel units first Reduce numbers to lowest terms. When the conversion equation is solved. Errors of omission are not indicated. * The text in red represents weak or erroneous technique. . rewrite as 25/100 with appropriate labels. form an equivalent relationship. and may have been omitted for that reason. There are errors of commission where students are taught flawed or even erroneous technique. A better rounded. Throughout the textbook. however. but come away feeling confident in their ability to handle any problems that may come their way in the future. Several medication math textbook titles are currently available. Overall. more robust presentation of dimensional analysis is definitely needed. There are errors of omission where students are not given a complete enough understanding of dimensional analysis to do all problems that could crop up. would have illustrated the shortcomings of the techniques as taught. . Students should not only do well solving test problems. but I think other titles should be looked into. I've heard that it is much better than its predecessor. overly simplified examples are used that fail to show the range of problems that students may encounter.Conclusions This may be a case of a book being the worst textbook on dimensional analysis available--with the exception of all the others. A wider range of problems. I would say that this book is quite useable provided its shortcomings and flaws are amended. however. but not having reviewed them. I can't assume any do a better job.