442 CHAPTER 7 The Metric System Suppose we want to convert 150 millimeters to inches. Table 7.7 does not have a conversion factor from millimeters to inches, but it does have one for inches to centimeters. Because 1 inch 2.54 centimeters = and 1 centimeter 10 millimeters, = we can reason that 1 inch 25.4 millimeters. = Therefore, unit fractions we may use are as follows. 1 in. 25.4 mm or 25.4 mm 1 in. We can solve the problem as follows. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ≈ 150mm (150 mm ) 1 in. 25.4 mm 150 25.4 in. 5.91 in. If we wish, we can use dimensional analysis using two unit fractions to make the conversion. The procedure follows: = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ≈ 150 mm (150 mm ) 1 cm 10 mm 1 in. 2.54 cm 150 (10)(2.54) in. 5.91 in. RECREATIONAL MATH What Metric Unit Am I? (a) I am a length greater than your foot, but less than the length of a large kitchen table top. (b) I am a weight greater than a calculator, but less than a rocking chair. (c) I am a liquid volume greater than a glass of water, but less than a large jug of milk or a gallon of gasoline. (d) I am an area greater than a football field, but less than the Magic Kingdom at Disney World. The answers are upside down below. (a) A meter (b) A kilogram Example 5 Administering a Medicine A nurse must administer 4 cc of codeine medicine to a patient. a) How many milliliters of the medicine will be administered? b) How many ounces is this dosage equivalent to? Solution a) Since 1 cc 1 m , = the nurse will administer 4 m of the medicine. b) Since 1 fl oz 29.5735 m , = = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ≈ 4 m (4 m ) 1 fl oz 29.5735m 4 29.5735 fl oz 0.14 fl oz 7 Now try Exercise 39 Example 6 Bicycle Tire Pressure The recommended tire pressure on Pascal’s new bicycle is 5 kilograms per square centimeter. Pascal’s tire gage only measures tire pressure in pounds per square inch. Convert the recommended tire pressure to pounds per square inch. Solution In this example, we need to convert kilograms to pounds and square centimeters to square inches. First, from Table 7.7, we see that 1 lb 0.4536 kg. = From this equation we form the unit fractions 1 lb 0.4536 kg or 0.4536 kg 1 lb . From Table 7.7, we see that 1 in. 6.4516 cm . 2 2 = From this equation we form the unit fractions 1 in. 6.4516 cm or 6.4516 cm 1 in. 2 2 2 2 We need our answer to have the units of pounds per square inch. We want pounds in the numerator and square inches in the denominator, so we perform the following dimensional analysis: ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = ≈ 5 kg cm 1 lb 0.4536 kg 6.4516 cm 1 in. 5(6.4516) lb 0.4536 in. 32.258 lb 0.4536 in. 71.12 lb in. 2 2 2 2 2 2 Therefore, the recommended tire pressure is about 71.12 pounds per square inch. 7 Now try Exercise 55 Shutterstock (c) A liter (d) A hectare
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