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: 1.2


28.9 cubic inches

Work Step by Step

Using only the given conversion factors, how could we get from liters to cubic inches? First we can use the conversion factor 1 L = 1000 cm^3 to convert from liters to cubic centimeters. The next part is tricky. The given conversion factor only gives inches to centimeters, but we want cubic inches and cubic centimeters. So what do we do? We cube the conversion factor! Now we have the conversion factor 1 in^3 = 2.54^3 cm^3 (don't forget to cube the conversion factor itself, as well as the units!). So now if we string this all together we get: 0.473 L x (1000 cm^3/L) x (1 in^3/2.54^3 cm^3) = 28.8642 in^3 Don't forget to cross out any units that appear in the top and bottom of the formula! L and cm^3 cancel, leaving us with units of in^3, or cubic inches, which is exactly what we want. Our answer should have the same number of significant figures as the question. The initial quantity, 0.473, has 3 sig figs, so we round the answer to 3, giving us 28.9 cubic inches.
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