University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 1 - Units, Physical Quantities, and Vectors - Problems - Exercises - Page 27: 1.1


a) 1.61 km b) 3280 feet

Work Step by Step

a) Before we start converting, it might be handy to map out how we will get from miles to kilometers. A good place to start would be miles to feet. We know that 5280 feet = 1 mile. Then from feet we could convert to inches. We know that 12 in = 1 ft. The given conversion factor (2.54 cm = 1 in) gets us from inches to centimeters. Now we just have to get from centimeters, to meters, to kilometers. You could go straight from centimeters to kilometers, but I find taking the extra step reduces errors. We know that 100 cm = m and 1000 m = 1 km. If we string all these together we get: 1.00 miles x (5280 ft/mile) x (12 in/ft) x (2.54 cm/in) x (1 m/100 cm) x (1 km/1000 m) = 1.6093 km If you cross out every unit that appears on both the top and bottom of the formula, you are left with units of kilometers, which is exactly what you want. Don't forget significant figures! If we reduce the answer to the number of significant figures in the question (there are 3 sig figs in 1.00 miles), we are left with 1.61 km. b) Same as up top, we'll start this problem by mapping out our conversion. An easy place to start is kilometers to meters. We know that 1000 m = 1 km. Then meters to centimeters at 100 cm = 1 m. Then we can use the given conversion factor 2.54 cm = 1 in. Now we have to convert from inches to feet and we're done. Strung together we get: 1.00 km x (1000 m/km) x (100 cm/m) x (1 in/2.54 cm) x (1 ft/12 in) = 3280.8398 feet Remember to cross out every unit that appears in the top and bottom of the formula, leaving you with units of feet. The question had three significant figures, so let's make sure our answer does as well. The correct answer is 3280 feet.
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