5.3: American Units to Metric Units and Vice-Versa
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- Feb 17, 2021
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We often need to convert from the American system of units to the metric system of units or vice-versa (imagine traveling to a European country using the metric system). That will be our focus in this section.
Converting Units of Length
One meter is slightly longer than one yard. Indeed,
1m≈1.0936yd.
If we divide both sides of this equation by 1.0936, then
1 m1.0936≈1.0936 yd1.09360.9144 m≈1 yd
Further conversions can be made. For example, to change meters to feet, we make the following conversions.
1 m ≈1 m ⋅1 yd0.9144 m⋅3 ft1 yd Apply conversion factors.≈1m⋅1 yd0.9144 m⋅3 ft1 yd Cancel common units.≈1⋅1⋅30.9144⋅1 ft Multiply fractions.≈3.2808 ft
Table 6.5 shows some of the most common conversions between American units of length and metric units of length.
American to Metric | Metric to American |
---|---|
1 in ≈ 2.54 cm | 1 cm ≈ 0.3937 in |
1 ft ≈ 0.3048 m | 1 m ≈ 3.2808 ft |
1 yd ≈ 0.9144 m | 1 m ≈ 1.0936 yd |
1 mi ≈ 1.6093 km | 1 km ≈ 0.6214 mi |
Example 1
A car’s speedometer shows that a family has currently traveled 154 miles in route to their vacation destination. Convert this distance to kilometers.
Solution
Choose 1 mi = 1.6093 km from Table 6.5.
154 mi ≈154 mi ⋅1.6093 km1 mi Apply conversion factor.≈154 mi⋅1.6093 km1 mi Cancel common units.≈154⋅1.60931 km Multiply fractions.≈247.8 km
Hence, 154 miles is approximately 247.8 kilometers.
Alternate Solution
Note that this would work equally well if we chose 1 km ≈ 0.6214 mi from Table 6.5.
154 mi ≈154 mi ⋅1 km0.6214 mi Apply conversion factor.≈154 mi⋅1 km0.6214 mi Cancel common units.≈154⋅10.6214 km Multiply fractions.≈247.8 km
Exercise
Change 227 miles to kilometers. Round to the nearest tenth of a kilometer.
- Answer
-
365.3 kilometers
Converting Units of Weight and Mass
It is known that
1kg≈2.2lb.
Dividing both sides of this equation by 2.2,
1 kg2.2≈2.2 lb2.20.454 kg≈1lb
A summary of the more common conversion factors regarding mass and weight are given in Table 6.6.
American to Metric | Metric to American |
---|---|
1 oz ≈ 28.35 g | 1 g ≈ 0.035 oz |
1 lb ≈ 0.454 kg | 1 kg ≈ 2.2 lb |
Example 2
Change 2.3 kilograms to ounces.
Solution
One kilogram weighs 2.2 pounds and there are 16 ounces in a pound.
2.3 kg ≈2.3 kg ⋅2.2 lb1 kg⋅16 oz1 lb Apply conversion factors.≈2.3 kg⋅2.2 lb1 kg⋅16 oz1lb Cancel common units.≈2.3⋅2.2⋅161⋅1 oz Multiply fractions.≈80.96 oz
Hence, 2.3 kilograms weighs 80.96 ounces.
Alternate Solution
Another approach uses the facts that 1 kilogram equals 1000 grams and 1 ounce equals 28.35 grams.
2.3 kg ≈2.3 kg ⋅1000 g1 kg⋅1 oz28.35 g Apply conversion factors.≈2.3 kg⋅1000 g1 kg⋅1 oz28.35 g Cancel common units.≈2.3⋅1000⋅11⋅28.35 oz Multiply fractions.≈81.13 oz
Roundoff Error
Why the discrepancy in answers? This difference in approximations is due to something called round-off error. Indeed, in the first calculation, we used a conversion factor that is rounded to the nearest tenth; i.e., 1 kg ≈ 2.2 lb. If we use a more accurate conversion factor to change kilograms to pounds, namely 1 kg ≈ 2.2046 lb, we get the following result.
2.3 kg ≈2.3 kg ⋅2.2046 lb1 kg⋅16 oz1 lb Apply conversion factors.≈2.3 kg⋅2.2046 lb1 kg⋅16oz1 lb Cancel common units.≈2.3⋅2.2046⋅161⋅1 oz Multiply fractions.≈81.13 oz
Note that this result is in better agreement with the second result above.
Exercise
Change 5.7 kilograms to ounces. Round to the nearest ounce.
- Answer
-
201 ounces
Important Observation
To obtain better approximations, you need to use a conversion factor that is more accurate. Any time you feel you need more accuracy, you might try an online conversion utility, such as the one at: www.france-property-and-information.com/metric_ conversion_table.htm
Converting Units of Volume
It is known that
1 qt ≈ 0.946 L.
Dividing both sides of this equation by 0.946,
1 L ≈ 1.06 qt.
Again, these conversion factors for volume have been well worked out by scientists. The more common conversion factors for volume are shown in Table 6.7.
American to Metric | Metric to American |
1 fl oz ≈ 0.030 L | 1 L ≈ 33.8 fl oz |
1 pt ≈ 0.473 L | 1 L ≈ 2.1 pt |
1 qt ≈ 0.946 L | 1 L ≈ 1.06 qt |
1 gal ≈ 3.785 L | 1 L ≈ 0.264 gal |
Table 6.7: Volume conversions: American — Metric.
Example 3
Change 2.5 dekalitres to gallons.
Solution
Recall that 1 daL = 10 L and 1 L = 0.264 gal.
2.5 daL ≈2.5 daL ⋅10 L1 daL⋅0.264 gal1 L Apply conversion factors.≈2.5 daL⋅10 L1 daL⋅0.264 gal1 L Cancel common units.≈2.5⋅10⋅0.2641⋅1 gal Multiply fractions.≈6.6 gal
Hence, 2.5 dekalitres is approximately equal to 6.6 gallons.
Exercise
Change 3.2 dekalitres to gallons.Round your answer to the nearest tenth of a gallon.
- Answer
-
0.8 gallons
Converting Units of Speed
Modern speedometers often show a car’s speed in both miles per hour and kilometers per hour.
Example 4
A car’s speedometer is showing it speeding along at 60 kilometers per hour. How fast is it traveling in miles per hour? Round your answer to the nearest mile per hour.
Solution
From Table 6.5, 1 km ≈ 0.6214 mi.
60kmh≈60kmh⋅0.6214 mi1 km Apply conversion factor.≈60kmh⋅0.6214 mi1 km Cancel common units.≈60⋅0.62141mih Multiply fractions.≈37.284mih
To round to the nearest mile per hour, identify the rounding and test digits.
Because the test digit is less than 5, leave the rounding digit alone and truncate. Thus, to the nearest mile per hour, the speed is approximately 37 miles per hour.
Exercise
A car's speedometer registers 45 kilometers per hour. Change this speed to miles per hour. Round your answer to the nearest mile per hour.
- Answer
-
28 miles per hour
Exercises
1. Use the conversion 1 in = 2.54 cm to convert 68 inches to centimeters, rounded to the nearest tenth of a centimeter.
2. Use the conversion 1 in = 2.54 cm to convert 42 inches to centimeters, rounded to the nearest tenth of a centimeter.
3. Use the conversion 1 in = 2.54 cm to convert 44 centimeters to inches, rounded to the nearest tenth of a inch.
4. Use the conversion 1 in = 2.54 cm to convert 22 centimeters to inches, rounded to the nearest tenth of a inch.
5. Use the conversion 1 mi = 1.6093 km to convert 79 miles to kilometers, rounded to the nearest tenth of a kilometer.
6. Use the conversion 1 mi = 1.6093 km to convert 39 miles to kilometers, rounded to the nearest tenth of a kilometer.
7. Use the conversion 1 yd = 0.9144 m to convert 1489 centimeters to yards, rounded to the nearest tenth of a yard.
8. Use the conversion 1 yd = 0.9144 m to convert 1522 centimeters to yards, rounded to the nearest tenth of a yard.
9. Use the conversion 1 yd = 0.9144 m to convert 28 yards to centimeters, rounded to the nearest tenth of a centimeter.
10. Use the conversion 1 yd = 0.9144 m to convert 34 yards to centimeters, rounded to the nearest tenth of a centimeter.
11. Use the conversion 1 m = 3.2808 ft to convert 8.6 meters to inches, rounded to the nearest tenth of a inch.
12. Use the conversion 1 m = 3.2808 ft to convert 8.3 meters to inches, rounded to the nearest tenth of a inch.
13. Use the conversion 1 in = 2.54 cm to convert 60 inches to centimeters, rounded to the nearest tenth of a centimeter.
14. Use the conversion 1 in = 2.54 cm to convert 75 inches to centimeters, rounded to the nearest tenth of a centimeter.
15. Use the conversion 1 m = 3.2808 ft to convert 208 inches to meters, rounded to the nearest tenth of a inch.
16. Use the conversion 1 m = 3.2808 ft to convert 228 inches to meters, rounded to the nearest tenth of a inch.
17. Use the conversion 1 m = 1.0936 yd to convert 20 yards to meters, rounded to the nearest tenth of a meter.
18. Use the conversion 1 m = 1.0936 yd to convert 44 yards to meters, rounded to the nearest tenth of a meter.
19. Use the conversion 1 mi = 1.6093 km to convert 29 miles to kilometers, rounded to the nearest tenth of a kilometer.
20. Use the conversion 1 mi = 1.6093 km to convert 15 miles to kilometers, rounded to the nearest tenth of a kilometer.
21. Use the conversion 1 m = 1.0936 yd to convert 8.2 meters to yards, rounded to the nearest tenth of a yard.
22. Use the conversion 1 m = 1.0936 yd to convert 6.9 meters to yards, rounded to the nearest tenth of a yard.
23. Use the conversion 1 mi = 1.6093 km to convert 4.9 kilometers to miles, rounded to the nearest tenth of a mile.
24. Use the conversion 1 mi = 1.6093 km to convert 4.2 kilometers to miles, rounded to the nearest tenth of a mile.
25. Use the conversion 1 m = 1.0936 yd to convert 25 yards to meters, rounded to the nearest tenth of a meter.
26. Use the conversion 1 m = 1.0936 yd to convert 2 yards to meters, rounded to the nearest tenth of a meter.
27. Use the conversion 1 in = 2.54 cm to convert 47 centimeters to inches, rounded to the nearest tenth of a inch.
28. Use the conversion 1 in = 2.54 cm to convert 19 centimeters to inches, rounded to the nearest tenth of a inch.
29. Use the conversion 1 mi = 1.6093 km to convert 8.3 kilometers to miles, rounded to the nearest tenth of a mile.
30. Use the conversion 1 mi = 1.6093 km to convert 4.8 kilometers to miles, rounded to the nearest tenth of a mile.
31. Use the conversion 1 yd = 0.9144 m to convert 41 yards to centimeters, rounded to the nearest tenth of a centimeter.
32. Use the conversion 1 yd = 0.9144 m to convert 20 yards to centimeters, rounded to the nearest tenth of a centimeter.
33. Use the conversion 1 m = 3.2808 ft to convert 3.7 meters to inches, rounded to the nearest tenth of a inch.
34. Use the conversion 1 m = 3.2808 ft to convert 7.9 meters to inches, rounded to the nearest tenth of a inch.
35. Use the conversion 1 yd = 0.9144 m to convert 1323 centimeters to yards, rounded to the nearest tenth of a yard.
36. Use the conversion 1 yd = 0.9144 m to convert 1715 centimeters to yards, rounded to the nearest tenth of a yard.
37. Use the conversion 1 m = 1.0936 yd to convert 8.4 meters to yards, rounded to the nearest tenth of a yard.
38. Use the conversion 1 m = 1.0936 yd to convert 7.3 meters to yards, rounded to the nearest tenth of a yard.
39. Use the conversion 1 m = 3.2808 ft to convert 289 inches to meters, rounded to the nearest tenth of a inch.
40. Use the conversion 1 m = 3.2808 ft to convert 251 inches to meters, rounded to the nearest tenth of a inch.
41. Use the conversion 1 kg = 2.2 lb to convert 15.8 kilograms to pounds, rounded to the nearest tenth of a pound.
42. Use the conversion 1 kg = 2.2 lb to convert 19.4 kilograms to pounds, rounded to the nearest tenth of a pound.
43. Use the conversion 1 oz = 28.35 g to convert 35 ounces to grams, rounded to the nearest tenth of a gram.
44. Use the conversion 1 oz = 28.35 g to convert 33 ounces to grams, rounded to the nearest tenth of a gram.
45. Use the conversion 1 kg = 2.2 lb to convert 2.48 kilograms to ounces, rounded to the nearest tenth of a ounce.
46. Use the conversion 1 kg = 2.2 lb to convert 3.74 kilograms to ounces, rounded to the nearest tenth of a ounce.
47. Use the conversion 1 kg = 2.2 lb to convert 2.35 kilograms to ounces, rounded to the nearest tenth of a ounce.
48. Use the conversion 1 kg = 2.2 lb to convert 3.57 kilograms to ounces, rounded to the nearest tenth of a ounce.
49. Use the conversion 1 kg = 2.2 lb to convert 15 pounds to kilograms, rounded to the nearest tenth of a kilogram.
50. Use the conversion 1 kg = 2.2 lb to convert 27 pounds to kilograms, rounded to the nearest tenth of a kilogram.
51. Use the conversion 1 kg = 2.2 lb to convert 10.4 kilograms to pounds, rounded to the nearest tenth of a pound.
52. Use the conversion 1 kg = 2.2 lb to convert 17.7 kilograms to pounds, rounded to the nearest tenth of a pound.
53. Use the conversion 1 kg = 2.2 lb to convert 352 ounces to kilograms, rounded to the nearest tenth of a kilogram.
54. Use the conversion 1 kg = 2.2 lb to convert 326 ounces to kilograms, rounded to the nearest tenth of a kilogram.
55. Use the conversion 1 oz = 28.35 g to convert 96 grams to ounces, rounded to the nearest tenth of a ounce.
56. Use the conversion 1 oz = 28.35 g to convert 100 grams to ounces, rounded to the nearest tenth of a ounce.
57. Use the conversion 1 oz = 28.35 g to convert 14 ounces to grams, rounded to the nearest tenth of a gram.
58. Use the conversion 1 oz = 28.35 g to convert 29 ounces to grams, rounded to the nearest tenth of a gram.
59. Use the conversion 1 kg = 2.2 lb to convert 54 pounds to kilograms, rounded to the nearest tenth of a kilogram.
60. Use the conversion 1 kg = 2.2 lb to convert 82 pounds to kilograms, rounded to the nearest tenth of a kilogram.
61. Use the conversion 1 oz = 28.35 g to convert 92 grams to ounces, rounded to the nearest tenth of a ounce.
62. Use the conversion 1 oz = 28.35 g to convert 103 grams to ounces, rounded to the nearest tenth of a ounce.
63. Use the conversion 1 kg = 2.2 lb to convert 388 ounces to kilograms, rounded to the nearest tenth of a kilogram.
64. Use the conversion 1 kg = 2.2 lb to convert 395 ounces to kilograms, rounded to the nearest tenth of a kilogram.
65. Use the conversion 1 qt = 0.946 L to convert 55.1 litres to quarts, rounded to the nearest tenth of a quart.
66. Use the conversion 1 qt = 0.946 L to convert 50.3 litres to quarts, rounded to the nearest tenth of a quart.
67. Use the conversion 1 L = 33.8 fl oz to convert 72073 fluid ounces to kilolitres, rounded to the nearest tenth of a kilolitre.
68. Use the conversion 1 L = 33.8 fl oz to convert 56279 fluid ounces to kilolitres, rounded to the nearest tenth of a kilolitre.
69. Use the conversion 1 L = 33.8 fl oz to convert 2.5 kilolitres to fluid ounces.
70. Use the conversion 1 L = 33.8 fl oz to convert 4.5 kilolitres to fluid ounces.
71. Use the conversion 1 qt = 0.946 L to convert 24 quarts to litres, rounded to the nearest tenth of a litre.
72. Use the conversion 1 qt = 0.946 L to convert 21 quarts to litres, rounded to the nearest tenth of a litre.
73. Use the conversion 1 qt = 0.946 L to convert 30 quarts to litres, rounded to the nearest tenth of a litre.
74. Use the conversion 1 qt = 0.946 L to convert 22 quarts to litres, rounded to the nearest tenth of a litre.
75. Use the conversion 1 gal = 3.785 L to convert 11.8 gallons to litres, rounded to the nearest tenth of a litre.
76. Use the conversion 1 gal = 3.785 L to convert 13.5 gallons to litres, rounded to the nearest tenth of a litre.
77. Use the conversion 1 gal = 3.785 L to convert 50.5 litres to gallons, rounded to the nearest tenth of a gallon.
78. Use the conversion 1 gal = 3.785 L to convert 55.9 litres to gallons, rounded to the nearest tenth of a gallon.
79. Use the conversion 1 L = 33.8 fl oz to convert 8.3 kilolitres to fluid ounces.
80. Use the conversion 1 L = 33.8 fl oz to convert 5.3 kilolitres to fluid ounces.
81. Use the conversion 1 qt = 0.946 L to convert 42.4 litres to quarts, rounded to the nearest tenth of a quart.
82. Use the conversion 1 qt = 0.946 L to convert 55.4 litres to quarts, rounded to the nearest tenth of a quart.
83. Use the conversion 1 gal = 3.785 L to convert 17.2 gallons to litres, rounded to the nearest tenth of a litre.
84. Use the conversion 1 gal = 3.785 L to convert 19.6 gallons to litres, rounded to the nearest tenth of a litre.
85. Use the conversion 1 L = 33.8 fl oz to convert 51274 fluid ounces to kilolitres, rounded to the nearest tenth of a kilolitre.
86. Use the conversion 1 L = 33.8 fl oz to convert 82164 fluid ounces to kilolitres, rounded to the nearest tenth of a kilolitre.
87. Use the conversion 1 gal = 3.785 L to convert 55.6 litres to gallons, rounded to the nearest tenth of a gallon.
88. Use the conversion 1 gal = 3.785 L to convert 59.2 litres to gallons, rounded to the nearest tenth of a gallon.
89. Change 60 miles per hour to kilometers per hour. Round your answer to the nearest kilometer per hour.
90. Change 56 miles per hour to kilometers per hour. Round your answer to the nearest kilometer per hour.
91. Change 77 miles per hour to kilometers per hour. Round your answer to the nearest kilometer per hour.
92. Change 57 miles per hour to kilometers per hour. Round your answer to the nearest kilometer per hour.
93. Change 42 kilometers per hour to miles per hour. Round your answer to the nearest mile per hour.
94. Change 56 kilometers per hour to miles per hour. Round your answer to the nearest mile per hour.
95. Change 62 kilometers per hour to miles per hour. Round your answer to the nearest mile per hour.
96. Change 63 kilometers per hour to miles per hour. Round your answer to the nearest mile per hour.
97. Tallest tower. The world’s tallest tower in Dubai has 160 floors at a height of 2, 717 feet. Convert the height of the tower to the nearest tenth of a meter. Associated Press-Times-Standard 02/09/10 World’s tallest tower closed a month after opening.
98. High peaks. For the first time, foreigners will be allowed to climb nearly 100 high-altitude Himalayan peaks on the Indian side of Kashmir, peaks ranging from 9, 840 feet to nearly 26, 246 feet. Convert the highest of the peaks to the nearest tenth of a meter. Associated Press-TimesStandard 04/11/10 India opens Himalayan peaks to foreigners.
99. Ancient find. In the southern Egyptian town of Luxor, a 3, 400-year-old 4-meter statue of Thoth, the ancient Egyptian god of Wisdom and Magic, was unearthed. Convert the height of the statue to the nearest tenth of a foot. Associated Press-Times-Standard 03/17/10 3,400-year-old statues unearthed in Egypt.
100. Arctic wind. Blizzard condition winds in the Arctic blew 80 miles per hour. Find the wind speed to the nearest kilometer per hour. Associated Press-Times-Standard 12/31/09 After 562-mile ski trek, seven women reach the South Pole.
101. Solar plane. The Solar Impulse lifted off from a military airport at a speed no faster than 28 miles per hour. Convert the speed of the solar-powered plane to the nearest kilometer per hour. Associated Press-Times-Standard 04/09/10 Solar-powered plane makes successful maiden flight.
Answers
1. 172.7 centimeters
3. 17.3 inches
5. 127.1 kilometers
7. 16.3 yards
9. 2560.3 centimeters
11. 338.6 inches
13. 152.4 centimeters
15. 5.3 meters
17. 18.3 meters
19. 46.7 kilometers
21. 9.0 yards
23. 3.0 miles
25. 22.9 meters
27. 18.5 inches
29. 5.2 miles
31. 3749.0 centimeters
33. 145.7 inches
35. 14.5 yards
37. 9.2 yards
39. 7.3 meters
41. 34.8 pounds
43. 992.3 grams
45. 87.3 ounces
47. 82.7 ounces
49. 6.8 kilograms
51. 22.9 pounds
53. 10.0 kilograms
55. 3.4 ounces
57. 396.9 grams
59. 24.5 kilograms
61. 3.2 ounces
63. 11.0 kilograms
65. 58.2 quarts
67. 2.1 kilolitres
69. 84500 ounces
71. 22.7 litres
73. 28.4 litres
75. 44.7 litres
77. 13.3 gallons
79. 280540 ounces
81. 44.8 quarts
83. 65.1 litres
85. 1.5 kilolitres
87. 14.7 gallons
89. 97 km/hr
91. 124 km/hr
93. 26 mi/hr
95. 39 mi/hr
97. 828.2 meters
99. 13.1 feet
101. 45 km/hr