YOU TRY 2 Convert each measurement to the indicated unit. a) 8000 lb to tons b) 1 1 2 qt to pints c) 12 sec to minutes d) 4.5 yd to feet 3 Use Unit Analysis to Convert Between Units Another way to convert between units is to use unit analysis. This method is commonly used in chemistry, nursing, and other science courses. Recall from our work with ratios that we can divide out common units that appear in the numerator and denominator of a fraction. For example, we can write the ratio 9 feet to 12 feet as 9 ft 12 ft 9 ft 12 ft 3 4 Divide 9 and 12 by 3. because the units divide out. In unit analysis, we divide out like units to help us convert between units and to guide us in performing the conversion correctly. Another concept we need to understand is that of a unit fraction. A unit fraction is a fraction that is equivalent to 1. The measurement equivalencies can be written as unit fractions. For example, we can think of the relationship 12 in. 1 ft as the ratio 12 in. to 1 ft. Then, we can write the ratio 12 in. 1 ft 12 in. 12 in. 1 12 in. 12 in. 1 1 1 1 So, 12 in. 1 ft is a unit fraction because it is equal to 1. All of the equivalencies in the table on p. 567 can be written as unit fractions. To convert from one unit of measurement to another, we will multiply the measurement we are given by the appropriate unit fraction. Write the equivalencies as unit fractions. Use unit analysis to convert 36 in. to feet. Solution First, identify the units we are given and the units we want to get. Since we are given inches and we want to get feet, write down the relationship between inches and feet: 12 in. 1 ft. Next, multiply the measurement we are given, 36 in., by the unit fraction relating 12 in. and 1 ft so that the inches divide out and we will be left with feet. 36 in. 1 ft 12 in. 3 in. 1 36 1 ft 12 1 in. Divide 36 and 12 by 12; divide out the unit of inches. 3 ft 1 Multiply. 3 ft Simplify. Therefore, 36 in. 3 ft. Let’s summarize the steps for converting from one unit to another using unit analysis. EXAMPLE 3 Write out the example on your own paper as you read it. www.mhhe.com/messersmith SECTION 7.1 Using U.S. Customary Measurements 569
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