7.4 Dimensional Analysis and Conversions to and from the Metric System 439 Conversions to and from the Metric System Now we will apply dimensional analysis to the metric system. Table 7.7 is used in making conversions between the U.S. customary system and the metric system. The values given in Table 7.7 are accurate to the nearest ten-thousandth, that is, to four decimal places to the right of the decimal point. We will use this table to obtain many unit fractions. Example 3 Using Several Unit Fractions Convert 60 miles per hour to feet per second. Solution Let’s consider the units given and where we want to end up. We are given mi hr and wish to end with . ft sec Thus, we need to change miles into feet and hours into seconds. Because two units need to be changed, we will need to multiply the given quantity by two unit fractions, one for each conversion. First we show how to convert the units of measurement from miles per hour to feet per second: ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ mi hr ft mi hr sec gives an answer in ft sec Since 1 hour contains 60 minutes and 1 minute contains 60 seconds, there are 60 60 3600 ⋅ = seconds in one hour. Now we multiply the given quantity by the appropriate unit fractions to obtain the answer: = ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ = = 60 mi hr 60 mi hr 5280 ft 1mi 1hr 3600 sec (60)(5280) (1)(3600) ft sec 88 ft sec Note that ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ ⎛ ⎝⎜ ⎞ ⎠⎟ 60 mi hr 1 hr 3600 sec 5280 ft 1 mi will give the same answer. 7 Now try Exercise 31 Learning Catalytics Keyword: Angel-SOM-7.4 (See Preface for additional details.) Table 7.7 Conversions Table Length 1 inch (in.) 2.5400 centimeters (cm) 1 foot (ft) 30.4800 centimeters (cm) 1 foot (ft) 0.3048 meter (m) 1 yard (yd) 0.9144 meter (m) 1 mile (mi) 1.6093 kilometers (km) Area 1 square inch (in.2) 6.4516 square centimeters (cm2) 1 square foot (ft2) 0.0929 square meter (m2) 1 square yard (yd2) 0.8361 square meter (m2) 1 square mile (mi2) 2.5900 square kilometers (km2) 1 acre (ac) 0.4047 hectare (ha) (Continued)
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