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# Scan_Doc0025 - equivalence statements 1 km = 1000m 1 m =...

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1.6 Dimensional Analysis 19 EXAMPLE 1.6 You want to order a bicycle with a 25.5-in frame, but the sizes in the catalog are given only in centimeters. What size should you order? SoLution You need to go from inches to centimeters, so 2.54 em = 1in is appropriate: 2.54 cm 25.5 in X 1 in = 64.8 cm SEE EXERCISES 1.41 AND 1.42 To ensure that the conversion procedure is clear, a multistep problem is considered in Example 1.7. EXAMPLE 1.7 A student has entered a 1O.0-km run. How long is the run in miles? SoLution This conversion can be accomplished in several different ways. Since we have the equiv- alence statement 1 m = 1.094 yd, we will proceed by a path that uses this fact. Before we start any calculations, let us consider our strategy. Wehave kilometers, which we want to change to miles. We can do this by the following route: kilometers ~ meters ~ yards ~ miles To proceed in this way, we need the following equivalence statements:
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Unformatted text preview: equivalence statements: 1 km = 1000m 1 m = 1.094 yd 1760yd = 1 mi To make sure the process is clear, we will proceed step by step: Kilometers to Meters 1000m 10.0 km X 1 km: = 1.00 X 10 4 m Meters to Yards 1.094 yd 1.00 X 10 4 rn X = 1.094 X 10 4 yd 1m Note that we should have only three significant figures in the result. Since this is an in-termediate result, however, we will carry the extra digit. Remember, round off only the final result. Yards to Miles- =vt we round to the correct num-nificant figures after each step e correct significant figures for lation. However, since you use ~~Tnr and combine steps on it, you d only at the end. 1mi 1.094 X 10 4 yd X 1760 yd = 6.216 mi Note in this case that 1 mi equals exactly 1760 yd by designation. Thus 1760 is an exact number....
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