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Home , Degree (angle), Dimensional analysis, Gram, Inch, Length, Long ton

1 Handout – Unit Conversions ()

The Metric had its beginnings back in 1670 by a mathematician called . The modern version, (since 1960) is correctly called "International System of Units" or "SI" (from the French "Système International"). The has been officially sanctioned for use in the since 1866, but it remains the only industrialized country that has not adopted the metric system as its official system of . Many sources also cite and Burma as the only other countries not to have done so.

This section will cover conversions (1) selected units Basic in the metric and American , (2) compound or derived measures, and (3) between metric and meter (m) American systems. Also, (4) applications using conversions will be presented. (g)

The metric system is based on a set of basic units and liter (L) prefixes representing powers of 10. (s)

(°C) or (°K) where C=K-273.15

Prefixes (The units that are in bold are the ones that are most commonly used.)

prefix symbol value giga G 1,000,000,000 = 109 ( a billion)

mega M 1,000,000 = 106 ( a million)

kilo k 1,000 = 103 hecto h 100 = 102

deca da 10

1 1 -1 deci d = 0.1 = 10 10 1 -2 centi c = 0.01 = 10 100 1 -3 milli m = 0.001 = 10 (a thousandth) 1,000 1 -6 micro μ (the Greek letter mu) = 0.000001 = 10 (a millionth) 1,000,000 1 -9 nano n = 0.000000001 = 10 (a billionth) 1,000,000,000

2

To get a sense of the of the basic units of meter, gram and liter consider the following examples.

The of a penny is 2.5 . The height of a door Almost everyone is familiar handle or knob is 1 meter. with 2 liter bottles of soda.

The next set of examples illustrates the use of some of the most used prefixes.

Examples: 1. 1 milligram = 1 gram = 0.001 gram, or 1 mg = g = 0.001 gram 1,000

2. 1000 mg=1g

3. 1 milliliter= 1 liter=0.001 liter, or 1 mL= L=0.001 L 1,000

4. 1,000 mL = 1 L

5. 1 centimeter= 1 meter=0.01 meter, or 1 cm = m = 0.01 m 100

6. 1 = 1,000 grams, or 1 kg = 1,000 g

7. 1 kilometer = 1,000 meters, or 1 km = 1000 m

8. 1 kilobyte = 1000 bytes (a byte is a unit used in computers to express the length of a “word”.)

9. 1 megabyte = 1,000,000 bytes = 1000 kilobytes

10. An adult male is about how tall? A) 175cm B) 175m C) 175mm

The correct answer is A) since he is almost twice the standard height of a door knob, so almost 2 meters, that is almost 200 cm.

11. Choose the most reasonable weight of a newborn baby: A) 3.7g B)13L C) 4kg D)0.4m

The correct answer is C) since 3.7g is like a penny, while L measures volume and m is for length.

3

Conversion Tables The American system of is based on the English system.

American-->American SI--> American Capacity (volume) 1 meter = 1.0936 = 3.2808 feet = 39.37 1 = 1gal = 4 = 4 qts 1 kilometer = .62137 1 = 1 qt = 2 = 2 pt 1 gram = .03527 1 = 1 pt = 2 cups = 2 c = 16 ounces = 16 fl oz 1 kilogram = 35.27 ounces = 2.205 pounds 1 = 1c = 8 fluid ounces = 8 fl. oz (Note: a fluid 1 liter = .26417 = 1.0567 quarts is not the same as the weight ounce.) 5 1 = 1 fl oz = 2 tablespoons = 2 tbsp CF  9  – 32 SI temperature measure is Celsius (°C). 1 tablespoon = 1 tbsp = 3 = 3 tsp freezes at 0 °C and boils at 100 °F Another SI measure Length for temperature is Kelvin (K) where 1 = 1 ft = 12 inches = 12 in 1 = 1 mi = 5280 feet = 1760 yd American--> SI Mass 1 = 0.0254 meters = 2.54 centimeters 1 = 1 lb = 16 ounces = 16 oz 1 = 0.9144 meters 1 = 2000 pounds = 2000 lb (This is sometimes called a 1 mile = 1609.344 meters = 1.609344 kilometers or ton(US). A or ton(UK) is equal to 1 pound = 453.59237 grams 2240 pounds.) 1 ounce 28.35 grams Temperature 1 gallon  3.784 liters Temperature is measured in degrees (°F). 1 quart  .9464 liters Water freezes at 32 °F and boils at 212 °F 1 fluid ounce  .02957 liters = 29.57 milliliters

1 tsp = 4.93 mL Everywhere in the World

Time 1 = 1 min = 60 = 60 s 1 = 1 hr = 60 min 1 = 24 hr

Small amount of Milliliters are used extensively in the and medicine. The “cc” is often used instead of mL. The relation of mL to volume is given by

4 and

Recall that is measured in squares. One foot or 1 ft2 represents the area covered by a square 1 foot by 1 foot.

Example: 1 2 3 4 12 square feet = 12 ft2 12 squares 1 foot by 1 foot. The measure of the area of a 3 ft by 4 ft is 12 ft2 since it can be covered (tiled) with 12 5 6 7 8 squares each 1 foot by 1 foot. 9 10 11 12

Volume is measured in . One cubic centimeter or 1 cm3 represents the volume that can be covered by a 1 cm by 1 cm by 1 cm.

Example: Find the volume of a box 3 cm by 3 cm by 4 cm. The question is, how many cubes 1 cm on a side can be put into this box. 3 cm × 3 cm × 4 cm = 36 cm3.

That is, the box will hold 36 cubes 1cm by 1 cm by 1 cm.

A conversion table could be made for areas and another could be made for volumes. The tables would include facts like 1 ft2 = 144 in2, 1 yd2 = 9 ft2, 1 m2 = 10000 cm2, 1 ft3 = 1728 in3, etc. Fortunately, as shown below, this is not necessary.

This handout will cover one method commonly used in the sciences to convert units. This method uses multiples of “1" in a convenient form.

Examples:

a) 4000 in = ? ft 1ft Notice that 1 ft = 12 in. We write our “1" as so that “in” in 4000 in will cancel. 12in 4,000in 1 ft 4,000 4,000in   ft  333.33 ft . notice that the “in” canceled 1 12in 12

b) 18 ft = ? in 18ft 12 in 18ft   216 in 11ft Notice that 1 ft = 12 in. This time we write our “1” as 12in / 1ft so that the “ft” cancel leaving only “in” as the unit.

c) 2.3 mi = ? in From the conversion tables on page 3 notice that 1 mi = 5280 ft and 1 ft = 12 in. So we should 5280푓푡 12푖푛 write our “1” in two different ways 1 = and as 1 = . Using the first fraction we can 1푚푖 1푓푡 convert miles into feet, while using the second fraction we can further convert the feet into inches. Combining these two we have the following:

5 2.3mi 5280 ft 12 in (2.3)(5280)(12) 2.3mi  in  145728 in 1 1mi 1 ft 1 notice that the “mi” and the“ft” cancel d) 146000 cm = ? km Just like in the previous example we don’t have a direct conversion between centimeters (cm) and kilometers (km). However, both are connected through meters (m). Therefore, we will use 1푚 1푘푚 the “1” in two different ways: 1 = and 1 = . Using both, we get the following: 100푐푚 1000푚 146000cm 1 m 1 km 146000 146000cm  km  1.46 km 1 100cm 1000 m (100)(1000) notice that the “cm” and the “m” cancel e) 1,000,000 fl oz = ? From the conversion tables on page 3, we see that 1 푝푡 = 16 푓푙 표푧, 1푞푡 = 2푝푡 and 1푔푎푙 = 4푞푡. We have to combine all three of these conversions to go from fluid ounces to gallons: 1000000fl oz 1 pt 1 qt 1 gal 1000000 1000000fl oz  gal  7812.5 gal 1 16fl oz 2 pt 4 qt (16)(2)(4) notice that the “fl oz”, the “pt”, and the “qt” cancel f) 18 ft2 = ? yd2 The following is the standard method for handling areas and volumes. The conversion tables on page 3 say that 1푦푑 = 3푓푡. For square units, we have to use this conversion twice so that “ft2" cancels with “ft∙ft”. 18ft2 1 yd 1 yd 18 18ft2  yd 2  2 yd 2 1 3ft 3 ft (3)(3)

Another way to obtain the same result is to create a new conversion for our specific prupose. Since 1푦푑 = 3푓푡 we immediately have 1푦푑2 = 3푓푡 ∙ 3푓푡 = 9푓푡2 and 18ft2 18 ft 2 1 yd 2 18ft22    2 yd 1 1 9 ft 2 g) 1,000,000 mm2 = ? km2 This time we will use two conversions 1 m = 1000 mm and 1 km = 1000 m. Each of these two conversion will be used twice, since we are using square units: 1000000mm2 1 m 1 m 1000000mm22    1 m Then we continue: 1 1000mm 1000 mm 11km km 1m2 1 m 2   0.000001 km 2 . Therefore 1000000푚푚2 = 0.000001푘푚2. 1000mm 1000 notice that “mm2" cancels with “mm mm” in the first row, and “m2” cancels with “m m” in the second row of calculations above. h) 18 ft3 = ? yd3 When dealing with cubic units, we have to apply each conversion formula three . For example, since 1푦푑 = 3푓푡, we can apply this conversion three times so that “ft3” cancels with “ft∙ft∙ft”. 18ft3 1 yd 1 yd 1 yd 18 2 18 ft3  yd 3  yd 3 1 3ft 3 ft 3 ft (3)(3)(3) 3

6 Or, as in the example f) above, we can create our own conversion formula 1yd33 3 ft  3 ft  3 ft  27 ft and use it directly: 18ft3 18 ft 3 1 yd 3 18 2 18 ft3    yd 3  yd 3 1 1 27ft3 27 3

i) 8 mL = ? cc This is a straight forward conversion, since 1푐푐 = 1푚퐿: 81mL cc 88mL cc 11mL

j) 3 L = ? cc This time we have to use two conversions in a row: 1 L = 1000 mL and 1 mL = 1 cc:

3L 1000 mL 1 cc (3)(1000) 3L  cc  3000 cc 1 1L 1 ml 1

k) 1 m3 = ? cc For cubic units, we use conversion three times: 3 3 1m 100 cm 100 cm 100 cm 1 cc (100)(100)(100) 1m3  cc  1000000 cc 1 1m 1 m 1 m 1 cm 1

Alternatively, we can derive our own conversion formula for cubic units. Using 1푚 = 100푐푚, we get. 1m33 100 cm  100 cm  100 cm  1000000 cm

l) 74 °F = ? °C

5 C = 9 (F – 32) 5 C = 9 (74 – 32) °C ≈ 23.3 °C

m) 29 °C = ? °F

9 F = 5 C + 32 9 F = [ 5 (29) + 32] °F = 84.2 °F

Compound Measures We now look at what is sometimes called compound measures: = mi/hr, ft/sec, lb/ft2, g/cm3 etc.

Examples

a) If a car is traveling 90 mi/hr, how many feet will the car travel in 1 sec? In 5 sec?

A direct way to convert these units is: 90mi 5280 ft 1 hr 1min (90)(5280) 90mi / hr  ft / sec  132 ft / sec 1hr 1 mi 60min 60sec (60)(60)

7 Alternatively, we can derive our own conversion formulas separately for miles and for : 1푚𝑖 = 5280푓푡 and 1ℎ푟 = 60푚𝑖푛 = 60 ∙ 60푠푒푐 = 3600푠푒푐. We then replace miles with 90mi 90 5280 ft 5280feet and hours with 3600sec. Therefore 132ft / sec hr3600 sec

In 1 second the car will travel 132 ft. The car will travel (5 sec )(132 ft/sec) = 660 ft. in 5 seconds.

b) A 90 lb weight is applied to an area 1/4 in by 1/4 inch. This is equivalent to how many per ft2 ?

We have 90 pounds per (1/4)(1/4) in2. We have [90 lb/(1/16) in2] = 1440 lb/in2.

21440lb 1 ton 12 in 12 in (1440)(12)(12) 2 2 1440lb / in2  ton / ft  103.68 ton / ft 1in 2000 lb 1 ft 1 ft 2000

c) If a machine produces 225 parts in an 8 hour day, how many will it take to produce 10 parts?

We will first get minutes per part. 8hours 60min 8(60) 32  min/part  min/ part 225parts 1 hour 225 15 The time needed for 10 parts would be (10)(32/15) minutes = 64/3 minutes = 21 minutes.

d) If a machine produces 225 parts in an 8 hour day, how many parts can it produce in 10 minutes ?

We will first get parts per minute. Notice that we have parts in the numerator since we want parts in the final answer. 225parts 1 hour 225 15  parts/ min  parts / min 8hours 60min 8(60) 32 15 75 11 In 10 minutes, the machine would produce 10 parts = parts =. 4 32 16 16

e) Water is pouring into a plastic box 1 m by 1 m by .3 m at the rate of 125 mL per minute. How long will it take in hours to fill this box?

The volume of the box is 1 m × 1 m × .3 m = .3 m3. In 1 minute, 125 mL will drip into the box. We will convert mL to cm3 to m3 and minutes to hours. 1min 1mL 100 cm 100 cm 100 cm 1 hr (100)(100)(100) hr hr       133.33 125mL 1 cm3 1 m 1 m 1 m 60min (125)(60) m 3 m 3

133.33 hrs for each m3. It will take (133.33)(.3) hr = 40 hr to fill the box

Homework:

2 2 3 3 1. 1000 yd = ? in 5. 1000 yd = ? in 9. 1000 yd = ? in

2. 2000 in = ? ft 6. 2000 in2 = ? ft2 10. 2000 in3 = ? ft3

3. 1000 in = ? yd 7 1000 in2 = ? yd 11. 1000 in3 = ? yd3

4. 2000 ft = ? in 8. 2000 ft2 = ? in2 12. 2000 ft3 = ? in3

8 13. 1,000,000 mm = ? cm 31. 50 mi = ? yd 49. 200 lb/in2 = ? tons/ft2

14. 1,000,000 mg = ? cg 32. 50 mi = ? in 50. 2.5 tons / ft2 = ? lb / in2

15. 1,000,000 mm = ? m 33. 1,000,000 tons = ? oz. 51. 100 km/hr = ? m/sec

16. 1,000,000 μg = ? g 34. 1,000,000 oz = ? tons 52. 250 m/min = ? km / hr

17. 1,000,000 mg = ? g 35. 1,000,000 fl. oz. = ? gal 53. 100 m/sec = ? km/hr

18. 1,000,000 cm = ? m 36. 1,000 fl. oz. = ? quarts 54. 250 km / hr = ? m / min

19. 1,000,000 mL = ? L 37. 42 °F = ? °C 55. 2 cc/sec = ? L/hr

20. 1,000,000 μm = ? cm 38. 73 °F = ? ° C 56. 2 L / hr = ? cc / min

3 21. 1,000,000 mm = ? km 39. 12 °C = ? °F 57. 2 m = ? L

3 22. 1,000,000 cm = ? km 40. 70 °C = ? °F 58. 18 L = ? m

2 2 23. 1,000,000 mg = ? kg 41. 25 °C = ? °K 59. 4 m = ? ft

2 2 24. 1,000,000 g = ? mg 42. 300 °K = ? °C 60. 4 ft = ? m

3 25. 1,000,000 km = ? m 43. 100 ft/sec = ? mi/hr 61. 9 qt = ? m

3 26. 1,000,000 kg = ? g 44. 100 mi / hr = ? ft / sec. 62. 2 m = ? qt

27. 1,000,000 km = ? cm 45. 5 gal / min = ? gal/hr 63. 1,000 kg= ? lbs

28. 1,000,000 mL = ? L 46. 5 pints / min = ? gal / hr 64. 35 lbs = ? kg

3 3 29. 1,000,000 kg = ? mg 47. 3 g/cm3 = ? kg/m3 65. 3.2 mg / mm = ? oz / in

3 30. 1,000,000 cg = ? g 48. 180 kg / m3 = ? g / mm3 66. 5 oz / in = ? mg / mm

67. A car traveling at a constant travels 71. If a car is traveling 75 miles per hour, how 175 miles in 4 hours. How many minutes will it many feet will it travel in 10 seconds ? take for the car to travel 1000 feet ? 72. If a car is traveling 75 kilometers per hour, 68. A car traveling at a constant speed travels how many meters will it travel in 10 seconds? 1000 ft in 12 seconds. In miles, how far will this car travel in 4 hours? 73. A leaky faucet drips at the rate of 1 pint per hour. How many gallons will drip in a 24 hour 69. A car traveling at a constant speed travels day? 175 miles in 4 hours. How many feet will the car travel in 10 minutes ? 74. A leaky faucet drips at the rate of 300 mL per hour. How many liters will drip in a 24 hour 70. A car traveling at a constant speed travels day? 1000 ft in 12 seconds. How long in hours will it take to travel 175 miles?

9 75. A leaky faucet drips at the rate of 1 pint per 86. A vehicle has a wheel 15 inches in . hour. How long will it take to fill a 10 gallon If the vehicle travels 2 miles, how many container? revolutions does the wheel make?

76. A leaky faucet drips at the rate of 300 mL 87. 1000 inches is how many meters? per hour. How long will it take to fill a 10 liter container? 88. 450 millimeters is how many inches?

77. You wish to give a patient 5 liters of fluid 89. A large block of butter measures 2.3 meters intravenously in 24 hours. If this is done at a by 3.4 meters by 5 meters. How many constant rate, how many cc must be given per tablespoons of butter are in this block? minute? 90. You wish to form a cube formed from 78. You wish to give a patient 4 liters of fluid in 1,000,000 tablespoons of butter. What is the 8 hours. If this is done at a constant rate, how length of a side in meters? feet? inches? (Recall: many cc must be given per minute? a cube has length = width = height.)

79. You are giving a patient 2.5 cc / min of a 91. An automatic machine produces 1 part every given solution intravenously. If this continues 2.3 minutes. How many parts are produced in 8 for 8 hours, how many liters of this solution will hours if the machine runs constantly? you need ? 92. A machine produces 4500 parts in an 8 hour 80. You are giving a patient 3 cc / min of a given day. In minutes, how long will it take to produce solution intravenously. If this is done for 24 100 parts? hours, how many liters of this solution will you need? 93. An automatic machine produces 1 part every 2.3 minutes. How long in hours will it take to 81. A recipe calls for 300 mL water. In the produce 5000 parts? English system, how much water is this? 94. If a machine produces 435 parts per hour. 82. A recipe calls for 3 cups water. In the metric how many minutes will it take to produce each system, how much water is this? part?

83. A car is traveling 100 km / hr, How many 95. A certain medication recommends that each feet does this car travel every second? day a person be given 8 mg for every 100 lbs of weight. John weighs 238 lbs. If his 84. A car is traveling 100 miles / hour. How measurements are exact, how many kg of this many meters does this car travel every second? medication will he take in 365 days? 85. John has a bicycle whose tires are 27 inches in diameter. If John rides his bike 1 mile, how 96. A certain medication recommends that each many revolutions does each tire make? day a person be given 8 mg for every 100 lbs of weight. If 10,000 people take this medication each day and their average weight is 180 lbs, how many of this drug are used daily?

10 Solutions:

1000yd 3 ft 12 in 1. 1000yd  (1000)(3)(12) in  36000 in 1 1yd 1 ft 1000in 1 ft 1 yd 1000 7 3. 1000in  yd  27 yd 1 12in 3 ft (12)(3) 9

1000yd2 3 ft 3 ft 12 in 12 in 5. (1000)(3)(3)(12)(12)in22 1296000 in 1 1yd 1 yd 1 ft 1 ft

1000in2 1 ft 1 ft 1 yd 1 yd 1000 7. yd22.77 yd 1 12in 12 in 3 ft 3 ft (12)(12)(3)(3)

1000yd3 3 ft 3 ft 3 ft 12 in 12 in 12 in 9. (1000)(3)(3)(3)(12)(12)(12)in33 46656000 in 1 1yd 1 yd 1 yd 1 ft 1 ft 1 ft

1000in3 1 ft 1 ft 1 ft 1 yd 1 yd 1 yd 1000 11. yd33.021 yd 1 12in 12 in 12 in 3 ft 3 ft 3 ft (12)(12)(12)(3)(3)(3)

1000000mm 1 m 100 cm (1000000)(100) 13. cm100000 cm 1 1000mm 1 m 1000

1000000mm 1 m 1000000 15. mm1000 1 1000mm 1000

1000000mg 1 g 1000000 17. gg1000 1 1000mg 1000

1000000mL 1 L 1000000 19. LL1000 1 1000mL 1000

1000000 mm 1 m 1 km 1000000 21.    km 1 km 1 1000 mm 1000 m (1000)(1000)

1000000mg 1 g 1 kg 1000000 23. kg1 kg 1 1000mg 1000 g (1000)(1000)

1000000km 1000 m 25. (1000000)(1000)mm 1000000000 11km

1000000km 1000 m 100 cm 27. (1000000)(1000)(100)cm  100000000000 cm  1  1011 cm 1 1km 1 m

1000000kg 1000 g 29. (1000000)(1000)gg 1000000000 11kg

50mi 5280 ft 1 yd (50)(5280) 31. yd88000 yd 1 1mi 3 ft 3

11 1000000tons 2000 lb 16 oz 33. (1000000)(2000)(16)oz  32000000000 oz  3.2  1010 oz 1 1ton 1 lb

1000000fl oz 1 pt 1 qt 1 gal 1000000 35. gal7812.5 gal 1 16fl oz 2 pt 4 qt (16)(2)(4)

5 5 9 9 37. C = 9 (F – 32) ; C = 9 (42 – 32) °C ≈ 5.6 °C 39. F = 5 C + 32; F = 5 (12) + 32 °F = 53.6 °F

41. K = C + 273.15; K = 25 + 273.15 °K = 298.15 °K

100ft 1 mi 60sec 60min (100)(60)(60) mi 5gal 60min 43. 68.18mi / hr 45. (5)(60)gal / hr 300 gal / hr 1sec 5280ft 1min 1 hr 5280 hr 1min 1hr

3g 1 kg 100 cm 100 cm 100 cm (3)(100)(100)(100) 47. kg/ m33 3000 kg / m 1cm3 1000 g 1 m 1 m 1 m 1000

200lb 1 ton 12 in 12 in (200)(12)(12) 49. tons/ ft22 14.4 tons / ft 1in2 2000 lb 1 ft 1 ft 2000

100km 1000 m 1 hr 1min (100)(1000) 51. mm/ sec 27.78 / sec 1hr 1 km 60min 60sec (60)(60)

100m 1 km 60sec 60min (100)(60)(60) 53. km/ hr 360 km / hr 1sec 1000m 1min 1 hr 1000

2cc 1 ml 1 L 60sec 60min (2)(60)(60) 55. L/ hr 7.2 L / hr 1sec 1cc 1000 ml 1min 1 hr 1000

2m3 100 cm 100 cm 100 cm 1 mL 1 L (2)(100)(100)(100) 57.      LL  2000 1 1m 1 m 1 m 1 cm3 1000 mL 1000

4m2 39.37 in 39.37 in 1 ft 1 ft 4(39.37)(39.37) 59.     ft22  43.05 ft 1 1m 1 m 12 in 12 in (12)(12)

9qt 1 L 1000 mL 1 cm3 1 m 1 m 1 m 9(1000) 61.       m3  .0085 1 1.0567qt 1 L 1 mL 100 cm 100 cm 100 cm (1.0567)(100)(100)(100)

1,000kg 2.2 lbs 63. 2,200lbs 11kg

3.2mg 1 g 1 kg 2.2 lbs 16 oz 1000 mm 1000 mm 1000 mm 1 m 1 m 1 m oz 65. 1.85 1mm33 1000 mg 1000 g 1 kg 1 lb 1 m 1 m 1 m 39.37 in 39.37 in 39.37 in in

4hours 1 mile 60min (4)(60) 67.   min/ft  .0002597min/ ft ; 175miles 5280 ft 1 hour (175)(5280) The car will take approximately .26 minutes to travel 1000 feet.

175miles 5280 ft 1 hour (175)(5280) 69.   ft/ min  3850 ft / min ; 4hours 1 mile 60min (4)(60)

12 In 10 minutes the car would travel (10)(3850) ft = 38500 ft.

75mi 5280 ft 1 hr 1min (75)(5280) 71.    ft 110 ft 1hr 1 mi 60 min 60 sec (60)(60) sec sec In 10 seconds the car will travel (10)(110) ft. = 1100 ft.

1pt 1 qt 1 gal 24 hours 24 73.    gal/3 day  gal 1hour 2 pt 4 qt 1 day (2)(4) day

1hour 2 pt 4 qt 75.    8/hours gal ; It would take (10)(8) hours = 80 hours to fill a 10 gallon container. 1pt 1 qt 1 gal

5L 1 hour 1000 mL 1 cc (5)(1000) 77.    cc/ min  3.47 cc / min 24hours 60min 1 L 1 mL (24)(60)

2.5cc 60min 1 mL 1 L (2.5)(60) 79.    L/ hour  .15 L / hour .You need (8)(.15) L = 1.2 L in 8 hours. 1min 1hour 1 cc 1000 mL 1000

300mL 1 pt 300 5 52cups 300mL 1 Tbs 81.  pt  pt , also pt1 1 cups and 10Tbs 1 480mL 480 8 81pt 4 1 30mL

100km .6214 miles 5280 ft 1 hr 1min (100)(.6214)(5280) ft 83.       91.14 ft 1hr 1 km 1 mile 60min 60sec (60)(60)sec sec

85. C = π d = 2 π r ; C = π 27 in. ; 1 revolution = 1 rev = 1 = 27 π in. ; 1mile 5280 ft 12 in 1 rev (5280)(12)    rev  747 rev 1 1mile 1 ft 27 in 27

1000in 1 m 1000 87.  m  25.4 in 1 39.37in 39.37

89. Volume = 2.3 m x 3.4 m x 5 m = 39.1 m3 ; 39.1m3 100 cm 100 cm 100 cm 1 mL 1 tbsp (39.1)(100)(100)(100)      tbsp  2,600,000 tbsp 1 1m 1 m 1 m 1 cm3 15 mL 15

1part 60min 60 parts 26.1 parts (8)(26.1) parts 91.     ; 208.8 parts in 8 hours 2.3min 1hr 2.3 hr 1 hour 8 hours

2.3min 1hr 2.3 hr hr (.0383)(5000) hrs 93.   .0383  ; 1part 60min 60 part part 5000 parts It will take approximately 192 hours to produce 5000 parts.

8mg 238 lbs 95. 19.04mg each day; 19.04mg each day x 365 days = 6949.6 mg 100lbs 1 6949.6mg 1 g 1 kg 6949.6   kg  .0069496 kg 1 1000mg 1000 g (1000)(1000) In one , John would take approximately .007 kg.