Math For ScienceScientific Notation Significant Digits Conversion Problems Metric Conversions Temperature Conversions Density Teacher Presentations, Student Notes, Worksheets, Quizzes, Answer Keys Math for Science: Scientific Notation MATH for SCIENCE Scientific Notation I. Scientists ~ 1. Deal with: 1. Some very large numbers 2. Some extremely small numbers These numbers can be quite cumbersome to work with. To make it easier scientists frequently use “Scientific Notation.” 2. Scientific Notation: 1. A numerical shorthand frequently used for writing very large and extremely small numbers. 3. Converting Decimal format to Scientific Notation format: 1. Scientific Notation sets up numbers with: a. Only the leading, non-zero digit/number to the left of the decimal point in the units place. b. All the remaining numbers are placed to the right of the decimal point. c. Then that number is multiplied by 10n. d. The power/exponent “n” will correspond to : i. the number of places. ii. the direction in which the decimal point was moved. e. The power “n” is: i. positive (+) when the original number is greater than 1. ii. negative (-) when the original number is less than 1. f. For numbers greater than 1: i. count the number of places the decimal point was moved to the left until you have only one non-zero number/digit to the left of the decimal point. ii. that number becomes the power/exponent that goes to the upper right of the 10n. Atlantic Union Conference Teacher Bulletin www.teacherbulletin.org Page 3 of 21 0. 2. 6. 2. Examples: # Moving the Decimal Pt. 1.Math for Science: Scientific Notation g.00126 .000084 0.00012 0. Converting Scientific Notation format to Decimal format: 1.15.00008. 3.org Page 4 of 21 .7 x 10-2 ii.4 54321 0. 123 iii.4 x 10-5 iii. Move the decimal point to the left to make the number smaller (less than 1).75 x 10-2 .8765 x 104 1. 8.43 x 105 7.2 x 10-4 3.00000003. Examples: # Moving the Decimal Pt.26 321 Atlantic Union Conference Teacher Bulletin www.23 x 102 4. count the number of places the decimal point was moved to the right until you have only one non-zero number/digit to the left of the decimal point.7 12 D.2 1234 1.26 x 10-3 . 4.680 321 h.001. 7. Examples: # Moving the Decimal Pt.8000.06.75 0.45 12345678 0. 98765 Moving the Decimal Pt. i.0000000345 iii. For numbers less than 1: i. Answer i. 12345 743.23 21 4.03. 0.8 x 104 2.067 0.0375 21 ii.680 x 103 ii.43000. Answer i. fill the counting loops in with zeros.153 x 102 iii. Answer i.000. 215. When you move the decimal point and there are no numbers left. the negative of that number becomes the power/exponent that goes to the upper right of the 10n. 0. For numbers with 10+n : a.0001.3 12 6.teacherbulletin. Move the decimal point to the right to make the number bigger (greater than 1). b. ii.3 68. ii. For numbers with 10 -n : a. 9.000.45 x 10-8 6.8765 4321 Answer 9. 1234 3. Examples: # i. 4680 1. with the base 10 number from step 2 12.5 x 105 2. 123 1.5 x 105 12.00029. Example: (2.2 x 3.985 x 10-3 Scientific Notation Format 15.85 x 103 (1. is required for the answer.485 x 104 14.850.3 x 10-2) (4. Stage 2 has 2 steps: These two steps are determined by which format.25 x 106 Scientific Notation Format 14. Step 3: Move the decimal point the number Step 3: Take the decimally formatted first of places and the direction indicated number and change it to Scientific n by the x 10 exponent. Multiplication: 1.850.25 x 101) (105) 12345 1.52 x 10-5 (2.85 x 103 14. this means you just add the powers/exponents.95 x 2.6 x 10-2) (8. (3. Step 2: Multiply the base 10 numbers together.0) (103 x 102) 12.52 x 10-5 . Computations with Scientific Notation ~ When multiplying or dividing with two or more numbers in Scientific Notation format.5 x 105 12. (Remember.85 x 103 Decimal Format 14.5 x 103) (5.50000.0 x 102) (2. decimal or Scientific Notation.) c.95 x 104) (2.952 x 101) (10-5) 2. B.250. Notation.3) (104 x 10-7) 15. Step 4: Fill in the blank loops/spaces with Step 4: Multiply the number from step 3 zeros. A.6) (10-3 x 10-2) 29. (8.000. Decimal Format Scientific Notation Format a. the process is done in two stages.3 x 4.0002952 3. b.5 x 105) (3. 2. (6.52 54321 Scientific Notation Format 29.2 x 10-3) (3.52 x 10-5 Decimal Format 29. (1. Examples: 1.985 x 10-3 www.5) (10-2 x 105) 14.3 x 10-7) (6. Step 1: Multiply the two leading numbers together.985 x 10-3 Decimal Format 15.Math for Science: Scientific Notation II.teacherbulletin. b. Stage 1 has 2 steps: a.org Page 5 of 21 Atlantic Union Conference Teacher Bulletin .5 x 5.485 x 101) (103) 1.952 x 10-4 0. 4 x 103 + 3.5734 x 10-2 Page 6 of 21 Atlantic Union Conference Teacher Bulletin www.42 4.888.92 x 104 → 1.0516 x 104 30516. 1.2 x 10-3 – (-5) = 80.3842 x 102 + 4.3 10-3 3.3048 x 107 = (3.723 x 102 + 972.5 2 6.000.5985 x 101) (10-3) 1. 9. 3.985 321 (1.Math for Science: Scientific Notation . 1.048 x 106 or 6.3 32.24 x 10-3 → 96.92 x 104 → 0.2 10-5 8.065734 4.0125 x 103 . each number MUST: a.015985 C.0125 x 103 4012.3842 x 102 138.28883 x 104 2.3 x 10-3 6. 4. F.0 102 1.2 x 102 = 8. Line up the decimal points.teacherbulletin.008126 0.3 3.385 x 10-2 0.2 x 103 or 1.015. Examples: 1. D.0.200 6. 3.126 x 10 .0516 x 104 + 9. Examples: 96.2 x 105 → 1. (Remember.6.5985 x 10-2 0.02 x 103 or 8020 1.965 x 101 49.156 1. Stage 1 has 2 steps: a. add or subtract the numbers.0 x 102 6.org .88156 x 102 7. Be converted back to decimal format.126 x 10-3 7. this means you just subtract the exponents/powers.07386 -3 8.8. 6.086 188.4 x 103 1400. 3.048.6 x 10-2 1.0 2.65 -2 8. Addition & Subtraction: 1. E. To add or subtract any numbers in Scientific Notation.637.723 x 102 1. b. Stage 2: Convert the result of stage 1 to either or both decimal format &/or Scientific Notation.2 x 105 → 8.5 3375. Division: 1.3750 x 103 3.965 x 101 + 8. c.385 x 10-2 .24 x 10-3 → 80.) 2.2 x 10-5 1. Then. 1. then b.375 x 102 4.375 x 10 .048 x 10-1) (107) = 3. Step 1: Divide the two leading numbers. Step 2: Divide the base 10 numbers.6 x 10 + . 5) of a point or one point.Math for Science: Scientific Notation Note for Teachers: The highlighted areas in the “Presentation” are the areas left blank in the “Student Notes.” It is recommended that each word or numbers the student successfully records on his/her “Notes” sheets be given either one half (0.org Page 7 of 21 . Giving students points for recording important information encourages them to stay focused during class and helps to ensure that students have complete information to study.teacherbulletin. Atlantic Union Conference Teacher Bulletin www.” These highlighted areas act as the grading “key” for the “Student Notes. dig. w = 8. the answer must www. A micrometer may be used to find the length of a microscopic object. 3 sig. 0.8 cm.60 x 10-3 # of Significant Digits 5 sig. h = 4. 2. Zeros between two nonzero digits (Trapped Zeros) 4. 3. the result can ______ have ________ significant digits than the measurement with the ___________ significant digits. For example: a. Also. To accurately reflect the instrument ’s level of precision. Scientific Notation # of Digits to Count All nonzero digits None of the leading zeros All of the trapped zeros. Thus. 3 sig. The _____________________ recorded for the answer must ____ indicate more _____________ than the tool/instrument being used is capable of measuring.org Page 5 of 13 Atlantic Union Conference Teacher Bulletin . 1 sig. dig. dig. 3. Nonzero digits 2. dig. a table scale accurate to milligrams may be used for small objects.000089 36. When doing multiplication and division calculations with measured numbers: 1.345 0.0200 5.Math for Science: Significant Digits Significant Digits ~ Student Notes Name: _______________________________ Date: _________________ Grade: _______________ II. The digits that _______ the last digit are considered the exact or ______ digits. width and height of a box are each measured to a tenth of a centimeter. 3 sig. but a kilometer may be used for measuring a road. Zeros following last nonzero digits (Trailing Zeros) 5. the ___________________________ recorded depends on the __________________ of the instrument. The length. dig. 5 sig. Zeros before nonzero digits (Leading Zeros) 3. but a floor scale accurate to just grams may be used for a large object. This would indicate that the instruments were capable of measuring to a ______________________ of a centimeter. Introduction: A.teacherbulletin.3 x 104 4.00678 0. 2 sig. The certain/exact digits and the one uncertain/estimated digit are called the ______________________.3 cm. plus the nonzero digits Trailing zeros are counted only if there is a decimal point All of the digits Examples 12. c. dig. There are different scales that can be used to find the mass of an object. The ______ digit is always an estimate and therefore is called the _____________ or estimated digit. 6 sig. Rules for Determining the Number of Significant Digits Type of Number 1. l = 12. For example. dig. When taking measurements. B. 2 sig.7 cm. the _______________ of each measuring ________________ determines the ________ that can be measured accurately. 4 sig. When these numbers are multiplied together the result is______________.0002 14003 700 4000. dig. dig. In science different instruments are used to take measurements. b. dig. 1. 2. When doing the calculations.19 g (__ sig. dig._____________ m2 This number must be rounded to ____ sig.375 = ____________ → __________ 3.org Page 6 of 13 . 60. dig.19674 + 142. 8. dig. d.1 + 4. 7. C. 25. Examples: 1. dig. __________ all the __________ along until the ______ when the ___________ answer is determined. dig. Since two of the numbers have only two significant digits. = _______ m2 2. dig.) = __________________ This number will be rounded to __ sig. dig.7 m (__ sig. 348.53 m (__ sig.) x 1. = ________ D.) = 46.517 ml (__ sig. dig. Counting the number of significant digits when adding and subtracting. = __________ ml 3.teacherbulletin. the answer must have only _____________________ – ____________ cm3.) = ____________ ml This number will be rounded to __ sig.68 = _______________ → __________ 2.341 + 3.256 = ____________ → ___________ E.3 ml/g (__ sig. 1.Math for Science: Significant Digits not go past the ___________________________.) x 3.73 ml (__ sig. dig. 12. Examples: 1. Significant Digits Worksheet Atlantic Union Conference Teacher Bulletin www.) ÷ 5. 2. The number of significant digits in the answer is _________________ by the measurement with the ____________ decimal places. Problem-Solving Scheme Given Data x Specific Fractional Equivalent(s) = What Your Looking For The units in the numerator of the first item (________________) determine the units for the ______________________ of the next fraction. Introduction ~ A. How many minutes are in five hours? Given Data: 5 hrs Atlantic Union Conference Teacher Bulletin www. Each step directs the set-up for the _____________________ until the goal units are reached. Some people use many proportions to do these conversions. Dimensional analysis requires students to understand _____ concepts. The most efficient and easiest method to understand is called ______________________________ or factor-label method. weight of an object would be 8 g and not just 8.org Page 8 of 25 . All standard or situational equivalents can be represented by _____________________. they will cancel each other out. C. 2. ______________________ must be used with their __________. For example: 1 minute = 60 seconds 1 minute 60 seconds or 60 seconds 1 minute ___________ 1 foot ____________ 1 foot = 12 inches __________ 12 inches or 1 meter = 100 centimeter __________ or 3. For example. This method can be quite confusing when there are multiple conversions to be done. and more. two steps. This method can be used for problems that are one step. The choice depends on what units are originally given in the problem. One Step Conversions 1. 1. moving one step at a time. This also. 4. B. chooses which one of the two forms of the specific fractional equivalents you will need to use. When these units are the _____________. three steps.Math for Science: Conversion Problems Conversion Problems ~ Student Notes Name: ____________________________________ Date: _____________ Grade: ________________ II. It can accommodate any number of ___________________ as one ________________________.teacherbulletin. In science many problems require conversions from one set of _________ to another. 1.Math for Science: Conversion Problems Fractional Equivalent: 1 hour = 60 min Looking For: # minutes 1 hour 60 min or 60 min 1 hour Given Data x Specific Fractional Equivalent = Looking For 5 hours x 60 min = 300 min 1 hour Notice how the “hour” units canceled each other out. will only let them enter the time in seconds. how many inches did he walk in that hour? Given Data: __________________ Specific Fractional Equivalents: 1 yard = 36 inches _________ or __________ 36 in 1 yd Looking For: ________________ Given Data x Specific Fractional Equivalent = Looking For 20 yards x ___________ = ______ inches 1 hr 1 yard 1 hr 3. How many grams will that weigh? Given Data: _______________ Specific Fractional Equivalents: 1 ounce = 28.teacherbulletin. One of their study observations took 5 hours. Two Step Conversions ~ Type 1 Remember the units in the previous _________________ will determine which form of the two _______________________________ will be used.33 grams __________ or __________ Looking For: ____________________ Given Data x Specific Fractional Equivalent = Looking For 6. How many seconds should they enter? Given Data: 5 hours Specific Fractional Equivalents: 1 hour = 60 minutes _____________ or _____________ Atlantic Union Conference Teacher Bulletin www.5 ounces x ____________ = ________________ grams D. .5 ounces.org Page 9 of 25 . A nugget of gold found in the river weighs 6. If a turtle walked 20 yards in one hour. Their computer program however. 2. Two students were using a computer program for their research data. Two Step Conversions ~ Type 2 These problems involve converting not just the numerator given. Convert 50 miles/hour to # kilometers/minute. Given Data: 50 miles/hour Specific Fractional Equivalents: 1 mile = 1. Given Data: ___________________ Specific Fractional Equivalents: 1 gram = 0.250 grams to # pounds.28 feet _____________ or ______________ 1 foot = 12 inches _____________ or ______________ Looking For: _______________ 2.Math for Science: Conversion Problems 1 minute = 60 seconds Looking For: # seconds _____________ or _____________ Given Data x Specific Fractional Equivalents = Looking For 5 hours x _________. Do the usual conversion of the numerator. by having the same units in the denominator and then in the later numerator.teacherbulletin. x _________ = ____________________ sec 1 hour 2. but also the denominator. Given Data: _________________ Specific Fractional Equivalents: 1 meter = 3.5 meters x ____________ x ____________ = ____________ inches E. 1. Then.250 grams x __________ x ____________ = _____________ lbs 3. the units once again will cancel each other out. the units in the original denominator determine the units in the later numerator. Convert 2. Thus.5 meters to # inches.61 km ___________ or _____________ Page 10 of 25 Atlantic Union Conference Teacher Bulletin www. 1. 2. Convert 2. convert the denominator.0353 ounces ______________ 16 ounces = 1 pound ______________ or or ______________ ______________ Looking For: ______________________ 2.org . To do this. 0353 ounces or 1 ounce = 28.teacherbulletin.org Page 11 of 25 . Convert 100 ounces/gallon to # grams/liter.2642 gallons or 1 gallon = 3.5 miles x 1. Given Data: _________________________ Specific Fractional Equivalents: 1 day = 24 hours ____________ or ____________ Atlantic Union Conference Teacher Bulletin www. The same sequence of actions would apply: change the numerator’s units. Given Data: _____________________ Specific Fractional Equivalents: 1 gram = 0. Convert 3 days to # seconds.Math for Science: Conversion Problems 1 hour = 60 min ___________ or _____________ 2. Convert 20 yards/minute to # inches/second. as well.33 grams 1 liter = 0. 1. Three Step Conversion Problems Remember the units in the previous numerator will determine which form of the two Fractional Equivalents will be used.785 liters Looking For: __________________ 100 oz x __________ x ___________ gal = ___________grams 1 gal oz 1L OR 100 oz x _______________ x _______________ = ______________ 1 gal G. then change the denominator’s units.61 km x 1 hr = 0.067 km 1 hour 1 mile 60 min 1 min 2. Some Problems may also include changing the denominator’s units. Given Data: ________ yd/min Specific Fractional Equivalents: 1 yard = 36 inches ___________ or ___________ 1 minute = 60 seconds ___________ or ___________ Looking For: # inches/second 20 yd x ___________ x 1 min 1 min 1 yd = _______ in 1 sec 3. 33 g = 1 oz _____________ or _____________ ____________ 16 oz = 1 lb _____________ or ____________ 2.Math for Science: Conversion Problems 1 hour = 60 minutes 1 minute = 60 seconds ____________ ____________ or or ____________ ____________ Looking For: ___________________ 3 days x 24 hrs x 60 min x 60 sec = _______________ sec 1 day 1 hr 1 min 2.org Page 12 of 25 .teacherbulletin. Given Data: _______________ Specific Fractional Equivalents: 1 km = 1. Convert 18 kilometers/hour to # meters/second. Convert 9. Given Data: ____________________ Specific Fractional Equivalents: 28.000 g x __________ x __________ x ___________ = ___________ 1 cm Atlantic Union Conference Teacher Bulletin www.000 grams/centimeter to # pounds/inch.000 m ___________ or 1 hr = 60 min 1 min = 60 sec Looking For: ____________________ 18 km x __________ x ___________ x __________ = ___________ 1 hr 3.54 cm = 1 in _____________ or ____________ Looking For: _____________________ 9. 0082 Ml = ? L 78 L = ? kl 1. 1.762. first.Math for Science: Metric Conversions Metric Conversion Worksheet Name: _________________________________________ Date: _____________ Grade: ___________ For the following conversions. 1. 6.91 cg = ? g 0. 11. 5. 5. linear conversion method.5 km = ? cm 487. 2. 12. 7. 2. 13. use the mathematical.org Page 9 of 16 .teacherbulletin.3 mg = ? kg 5.17 m = ? cm 0.56 dm = ? μm 147 cg = ? mg 0. 15.4 hl = ? dl 3. 6. 3. 8. 4. 13.318 kg = ? dg 3. ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ Atlantic Union Conference Teacher Bulletin www. 9. 8. then.063 Mg = ? dag 25 dg = ? hg 14. 4. 3. 14. 14. Attach the work for the linear conversion to the back of this sheet. do the conversions using the chart method. 10. 9.750 μm = ? m 3. 12. 11.0072 dal = ? ml 8. 10. 7.5 ml = ? L 0. 15. 100. 0. Micro.1. 10-3 B.001.001. kilo. _____ Which of the following represents the prefix and values for “a?” A. 1.000.000. 0.0000001.000. Mega.1. 101 B. Milli. 1. hecto.Math for Science: Metric Conversions Metric Conversion Quiz Name: ______________________________________ Date: ________________ Grade: ___________ 1. Mega. 1.000. 106 D. 10-3 Which of the following represents the prefix and values for “d?” A. 103 C. _____ 4.teacherbulletin. 0.000001.org Page 12 of 16 2. deci. 10-6 B. deci.000. 10.000. .000. 10-1 D. 101 Which of the following represents the prefix and values for “c?” A. Milli. hecto. _____ Atlantic Union Conference Teacher Bulletin . 0. 1. deci. Mega. 10-1 C.000. 103 D. 103 www. _____ 3. 105 B. 0. 10-6 D. deka.000. 106 C. 106 Which of the following represents the prefix and values for “b?” A. Micro. 1. deka. Maga.01. 10-3 C. 10.000. 0. 100. hecto. 102 B. 0.1. A. _____ 9.73 dg Convert 0. 0. 62500 μg B. _____ 10.00437 cg Convert 4. Milli. 10-2 C. 0. deka. 100 D. A. Mega.510.00000437 cg C. 10-2 Which of the following represents the prefix and value s for “f?” A. 10-1 Which of the following represents the prefix and values for “g?” A. 0. A. 0.300 dg D. _____ 13. deka. kilo. 0. 10. 1. hecto.000 C. 2. deci. 1. _____ Atlantic Union Conference Teacher Bulletin . 85.000 15. 10-3 D. 10-3 B.teacherbulletin. 10. 43. _____ 8.0852 Mm C.437 kg to # cg. deci. 437 cg B.000852 Mm B.700 cg D. Milli. 103 Which of the following represents the prefix and values for “h?” A. _____ 12. 27. 0.org Page 13 of 16 6. centi. 1 Kg equals __________ grams. centi.273 dg B. 103 C. Micro. _____ 7.200 Mm D. 0. 1. 27.00004951 dal 1 meter equals ________ cm. 625 μg D.01. _____ 14. 495. 101 D. 8.0000625 μg 11.4951 dal C.5 mg to # μg. 0.0625 μg C.1 www. 1. centi. _____ Convert 8.951 ml to # dal.000. 100. 0. 101 C.000 dal B.001.001. hecto.001. 10 C.520 Mm Convert 62. _____ Which of the following represents the prefix and values for “e?” A. 102 B. A. 0.01 B. 100 B. A.000.Math for Science: Metric Conversions 5. 49. deci. 100. 1. A. 101 D. A. 0.000.1.52 hm to # Mm. 100 B.001 D. 0.1 dal D. 0. 0. 0. 0. 103 C. 0. 10-3 D.3 dg C. 102 Convert 273 mg to # dg. 1. 100. 10. ________________ C. – 20 oC 18. 18. 14. ________________ ________________ ________________ ________________ 13.2 oC o 2. 8. ________________ Convert the following Celsius temperature to Fahrenheit degrees and then to Kelvin degrees. 8. 177 oC 35 oC 25.teacherbulletin. 17. – 63 oF 1. 19. 10. 40.32) 9 o C = 5(40) 9 o C = 22. _______________ _______________ _______________ _______________ _______________ 2. -243. 65 oF 25 F 100 oF . 5. 308 oK 120 oK 28. 14. 13.6 oK 238 oK Kelvin 450 oK 22.32) 9 o C = 5(33) 9 o C = 18. – 153 oC 27. o C = 5(10 -.2 + 273 o K = 260.org Page 8 of 13 . 1.3 oK K = 22.2 oK Atlantic Union Conference Teacher Bulletin www. 95 oF 26. 10 oF 72 F 0 oF 85 oF 50 oF o 1. 313. 4. Complete the chart below with the missing temperatures. 11. 15. 16.32) 9 o C = 5(-22) 9 o C = -12.3 + 273 o K = 291. 20.6 oC 29. 6. 15. ________________ ________________ ________________ ________________ 10. o C = 5(72 -.2 oC o o K = -12.Math for Science: Temperature Conversions Temperature Conversions Worksheet Answer Key Name: __________________________________ Date: ___________________ Grade: ____________ A. 3. 9.2 + 273 K = 295. 70 C 20. 6. 350 oF 23. Fahrenheit Celsius 21. 9. 4. 19.7 oK K = 18. B. – 35 oC 105 oF 24. 3. 17. Convert the following Fahrenheit temperatures to Celsius degrees and then to Kelvin degrees.10 oF 110 oF o 2.3 oC o 3. – 10 oC 11.4 oF 30. 16. o C = 5(65 -. 0 oC 25 oC 60 oC o 12. 7. 7. 18 oC 42 oC 10 oC 32 C o _______________ _______________ _______________ _______________ _______________ 12. 5. 8 oK C = 5(85 .3 oK o F = 9(-10) + 32 5 o F = -18 + 32 o F = 14 oF o o 12.273 C = 177 oC K = 32 + 273 K = 305 oK K = 70 + 273 K = 343 oK www.7 oK 11.3 + 273 o K = 249. K = 0 + 273 K = 273 oK 13. o F = 9(32) + 32 5 o F = 57.org Page 9 of 13 Atlantic Union Conference Teacher Bulletin .8 + 273 K = 310.6 + 32 o F = 107. o F = 9(-20) + 32 5 o F = -36 + 32 o F = .32) 9 o C = 5(68) 9 o C = 37. o F = 9(25) + 32 5 o F = 45 + 32 o F = 77 oF o o F = 9(42) + 32 5 o F = 75.9 oC o 5. o C = 5(100 .4 oF o o K = 60 + 273 K = 333 oK 20.8 oC o 6. o K = -23.8 + 273 o K = 255.teacherbulletin. F = 9(18) + 32 5 o F = 32.4 oC o C = 5(-10 .32) 9 o C = 5(78) 9 o C = 43. o C = 5(0 . o K = 20 + 273 K = 293 oK C = 5(110 . o C = 5(25 .6 + 32 o F = 89.32) 9 o C = 5(18) 9 o C = 20 oC o o K = 29. K = 10 + 273 K = 283 oK 21. o K = 37.3 oC o 9.32) 9 o C = 5(53) 9 o C = 29.4 oF o 14. o K = 25 + 273 o K = 298 oK 17.9 + 273 o K = 269.4 + 32 o F = 64.4 oK 10.Math for Science: Temperature Conversions 4.32) 9 o C = 5(-42) 9 o C = -23.8 oC o o K = -3.4 + 273 o K = 302. o K = 42 + 273 K = 315 oK F = 9(60) + 32 5 o F = 108 + 32 o F = 140 oF o o F = 9(10) + 32 5 o F = 18 + 32 o F = 50 oF o o 18.32) 9 o C = 5(-7) 9 o C = -3.32) 9 o C = 5(-32) 9 o C = -17. o C = 5(50 .1 oK 7. o K = -17. o F = 9(0) + 32 5 o F = 32 oF o o K = -10 + 273 K = 263 oK 15.6 oF o o o F = 9(70) + 32 5 o F = 126 + 32 o F = 158 oF o o o o C = 450 . K = -20 + 273 K = 253 oK 19.3 + 273 o K = 316.2 oK 8.3 oC o K = 43.6 oF o o K = 18 + 273 o K = 291 oK 16. 21. o F = 9(35) + 32 5 o F = 63 + 32 o F = 95 oF o 24. 20.Math for Science: Temperature Conversions 22.275. 17. F = 9(-153) + 32 5 o F = . C = 120 – 273 C = . 3.6 + 273 o K = 313.243.6 oK 29. 4.4 oF o 27. o F = 9(177) + 32 5 o F = 318. 14. 23. 19. 28. 2.4 + 32 o F = . 30. Totals Atlantic Union Conference Teacher Bulletin www. 6. 26.31 oF Correct Answer (1 pt each) Total Points (4 pts each) (120 pts Possible) Worksheet Grading Rubric: # Correct 1st Equation (1 pt each) 120/120 Points Correct Calculations (1 pt each) Correct 2nd Equation (1 pt each) 1.63 + 32 o F = . 9. 11. 8. 27. 5.6 + 32 o F = 350. 7. 25.org Page 10 of 13 . 29. 10. 16.35) + 32 5 o F = .6 oF o o 23.153 oC 26. 15. 18. o o K = 35 + 273 K = 308 oK 25.35 oC 30.6 oC o 28. 22.teacherbulletin. 24. 12. F = 9(. 13. C = 238 – 273 o C = . o C = 5(105 – 32) 9 o C = 5(73) 9 o C = 40. o K = 40. Math for Science: Density Density ~ Student Notes Name: ____________________________________ Date: ________________ Grade: _____________ I. so the smaller gram and cm3 units are used for everyday laboratory measurements and calculations. The SI units are __________________ for mass and ______________ for volume. For example. This means the ____________ is always the _______ for each specific substance. when one _______________ so does the other.5 3 2. Conversely.5 0 1 4 3 2 1 Mass (g) 2 3 Volume (ml) 4 5 Atlantic Union Conference Teacher Bulletin www. This means whenever one of the units_____________ . 2. B. In the metric system.5 4 3. forms of liters or forms of meters cubed. This slope is always __________ for a specific substance regardless of the _______ or _________ of the object. _____________ can be expressed by _____ different sets of units. the commonly used units for mass are __________ and for volume are _________________________________.teacherbulletin. D. F.5 2 1. The equation for this relationship is: Density = Mass of a substance Volume C. Water Density 5 4. so does the other one.5 1 0. These SI units are very large. _____________ thus becomes a tool to ________ what substance is present. In chemistry.org Page 6 of 15 . Mass and volume units are ____________________ proportional. For example. Density Defined ~ A. Density is a _____________________ that relates a ratio of the mass of a substance to its unit volume. These two units are_____________________ . _______________ = ________________________ . 1. D = ____ E. 3. the graph below demonstrates that the _______ of mass/ volume _______ the ________ of the line. A decorative copper pin displaced a volume of 3. 1. ____________ both sides by volume (V).5 cm wide by 1. what is iron’s density? a. and 4.4 grams.2 cm wide. To solve for volume: a.1 grams. D=? D=M D= g M = ______ g V cm3 V = ______ cm3 D = _______ g/cm3 H. The ___________________ can be manipulated to solve for either ______ or ______. leaving volume (V) by its self. V=? V = LWH L = ______ cm V = (______ cm)(______ cm)(______cm) W = ______cm V = _______ cm3 H = ______ cm b.4 g V cm3 3 V = 58. A rod of iron measures 6. 2. ____________ both sides by density (D). To solve for mass: a.Math for Science: Density G.teacherbulletin. The three resulting equations are: D=M M=V*D V=M V D To find To find To find Density Mass Volume Examples. Atlantic Union Conference Teacher Bulletin www. V *D = M V=M D D D 3. V *D = M * V V*D=M V b.0 cm high weighs 7.63 cm 2. V*D=M*V V*D=M or M=V*D V 2. _____________ both sides by volume (V). What is the density of sugar? a. This will cancel the density on the left side of the equation.92 g/cm3? D = 8. D=? D=M D= g D = ___g/cm3 M = 461. What’s this pin’s mass given copper’s density is 8. Find the rod’s volume.92 g/cm3 M=V*D M=? M = (_____ cm3)(____ g) M = ______ g 3 V = 3.2 cm V = __________ cm3 H = 4.org Page 7 of 15 .1 cm b.1 cm high.5 cm long. A sugar cube (sucrose) measuring 3.5 cm 1 cm3 3. like you did in the previous step.5 cm V = (_____ cm)(______ cm)(______ cm) W = 2. This will cancel the volume in the denominator.0 cm long by 1. If the iron rod weighs 461.5 cm3. V=? V = LWH L = 6. 1. 5 cm V = _________ cm3 5.8 = ________ V = ________ ml D = M = ______ g V ml D = ________ g/ml c. a. Then the students wanted to find out how much each liquid weighed.8 ml.6 – 15. What is its volume? The density of table salt is 2. liquid B measured 4. Liquid A D=? M = 20. V=? V = r2 h r = 2 cm V = (______)(_____ cm)2(_______ cm) h = 8.6 ml.8 = _____ g V = _______ ml D = M = ______ g V ml D = ________ g/ml Results: b. The cylinder with liquid C weighed 22.2 grams.8 grams. Now. They had already weighed the empty graduated cylinders and each weighed 15. A cylinder container filled with table salt (sodium chloride) has hardened.9 – 15. Liquid A measured 3. a.16 g/cm3. calculate the density for each liquid to determine if the liquids are the same or different.Math for Science: Density 4. The cylinder with liquid A weighed 20.org Page 8 of 15 . Students in a lab were given 3 test tubes with clear liquid in each. Liquid B D=? M = 22. The students were told to determine if the test tubes have the same or different substances.8 = _______g V = _________ ml D = M = _______ g V ml D = _________ g/ml _____________________________________________________.teacherbulletin. Find the mass of the salt in the cylinder.1 ml. The cylinder has a diameter of 4 cm and a height of 8.5 cm.2 – 15.9 grams. Atlantic Union Conference Teacher Bulletin www. and liquid C measured 4.6 grams. The liquid in each of the 3 test tubes was poured into 3 graduated cylinders. Liquid C D=? M = 22. The cylinder with liquid B weighed 22. They were told to find its volume and mass. Block B measures 2. 6. 9. Block A measures 3 cm long by 1. Show all work. The cylinder weighs 400 g. 10.5 ml Density 1.81 g/ml 5. Atlantic Union Conference Teacher Bulletin www. which has a density of 1. 8. and which is salt (sodium chloride).43 g/ml 2.87 g/cm3. 5. 4. After carefully measuring the block’s dimensions at 15 cm long by 8 cm wide by 12 cm high.68 g/ml 9. 7. black cylinder and asked to determine if it is iron or some other metal.16g/cm3.) Find the mass.24 g/ml Students were given a block of salt. They must determine which block is sugar (sucrose). 3.5 cm wide by 4 cm high and weighs 28.58 g/cm3.5 g Volume 300 ml 120 ml 535 ml 47. How can they still find the mass of the block even though it is dissolving in the pot of water? (Hint: Salt’s density is 2. # 1. they remembered they were supposed to weigh the block BEFORE they put it in the water.Math for Science: Density Density Quiz Name: ______________________________________ Date: _______________ Grade: ____________ Complete the chart by solving for the missing data. Suddenly. Students are given a solid. Iron’s density is 7.26 ml 65.org Page 13 of 15 .16 g/cm3. they put the block in water.4 g 48. which has a density of 2. Students are given 2 tiny blocks of white substances. 2.5 g.4 g. Mass 250 g 65 g 620 g 137.teacherbulletin.5 cm long by 2 cm wide by 3 cm high and weighs 32. The cylinder has a diameter of 3 cm and a height of 7 cm.
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