7.4 Dimensional Analysis and Conversions to and from the Metric System 437 Understand Unit Fractions You may sometimes need to change units of measurement in the metric system to equivalent units in the U.S. customary system or vice versa. To do so, use dimensional analysis, which is a procedure used to convert from one unit of measurement to a different unit of measurement. To perform dimensional analysis, we begin with a discussion of unit fractions. A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1. From Table 7.6, we can obtain many unit fractions involving U.S. customary units. Why This Is Important The many examples and exercises in this section will provide opportunities to use dimensional analysis to convert units. Many of these conversions may be helpful to you in your everyday life. Table 7.6 U.S. Customary Units 1 foot 12 inches 1 yard 3 feet 1 mile 5280 feet 1 pound 16 ounces 1 ton 2000 pounds 1 cup (liquid) 8 fluid ounces 1 pint 2 cups 1 quart 2 pints 1 gallon 4 quarts 1 minute 60 seconds 1 hour 60 minutes 1 day 24 hours 1 year 365 days Examples of Unit Fractions 12 in. 1 ft 1 ft 12 in. 16 oz 1 lb 1 lb 16 oz 60 min 1 hr 1 hr 60 min In each of these examples of unit fractions, the numerator and the denominator are equal measures, so the numerical value of the unit fraction is 1. Dimensional Analysis To convert an expression from one unit of measurement to a different unit, multiply the given expression by the unit fraction (or fractions) that will result in the answer having the units you are seeking. When two fractions are being multiplied and the same unit appears in the numerator of one fraction and in the denominator of the other fraction, that common unit may be divided out and eliminated. For example, suppose we want to convert 30 inches to feet. We consider the following: = 30 in. ? ft
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