438 CHAPTER 7 The Metric System Since inches are given, we will need to eliminate them. Thus, inches will need to appear in the denominator of the unit fraction. We need to convert to feet, so feet will need to appear in the numerator of the unit fraction. If we multiply a quantity in inches by a unit fraction containing feet/inches, the inches will divide out as follows, leaving feet. In the following illustration we have omitted the numbers in the unit fraction so we can concentrate on the units. ⎛ ⎝⎜ ⎞ ⎠⎟ = ( in. ) ft in. ft Thus, to convert 30 inches to feet, we do the following. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = = 30 in. (30 in. ) 1 ft 12 in. 30 12 ft 2.5 ft Examples 1 through 3 do not involve the metric system. After that, we will use dimensional analysis to make conversions to and from the metric system. Throughout this section, when necessary, we will round our answers to the nearest hundredth. Example 1 Using Dimensional Analysis A billboard on the side of a road indicates that a restaurant is 420 feet ahead. Convert 420 feet to miles. Solution From Table 7.6 we see that 1 mile is 5280 feet. Therefore, we solve the problem as follows. = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ≈ 420 ft (420 ft) 1 mi 5280 ft 420 5280 mi 0.08 mi Thus, 420 feet is approximately 0.08 mile. 7 Now try Exercise 27 Example 2 Argentine Pesos While visiting Buenos Aires, Rosa paid 23,900 Argentine pesos for dinner for herself and a group of friends. At the time, one U.S. dollar could be exchanged for 268.37 Argentine pesos. Determine the cost of the dinner in U.S. dollars. Solution = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ≈ 23,900 pesos $1.00 268.37 pesos $23,900 268.37 $89.06 Thus, in U.S. dollars, the dinner cost about $89.06. 7 Now try Exercise 29 If more than one unit needs to be changed, more than one multiplication may be needed, as illustrated in Example 3. m Buenos Aires, Argentina SC Image/Shutterstock
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