Unit Conversions

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7 Solutions to Example Problems1. Look in the table and find the conversion that relates inches and centimeters:1in=2.54cm. The two possible unit multipliers are1in2.54cm and 2.54cm1inWe are trying to get rid of the inches, so we need to use the secondmultiplier:12in1× 2.54cm1in= 12 × 2.54cm = 30.48cm2. Looking in the table, you’ll see that there is no equation directly relatingyards and inches. However, there is one relating yards and feet, and onerelating feet and inches. So our path will be yd→ft→in.3 yd1 × 3 ft1 yd × 12in = (3 × 3 × 12)in = 108in1ft3. Because there is no equation in our table which directly relates kilometersand miles, we need to find a chain of conversions which will get us there.We need to follow the path km→m→cm→in→ft→mi.10✟ ✟ km1× 1000✚m1✟km✟× 100 ✟✟ cm1✚m × 1 in2.54✟✟ cm × 1 ft12in ×1mi5280ft =10 × 1000 × 100mi ≈ 6.21mi2.54 × 12 × 52804. Be very careful here because the gallon is a unit of volume. Again, welook in the table and find that we can convert from gallons to liters. Fromliters we can convert to milliliters; from milliliters to cubic centimeters;and from cubic centimeters to cubic inches. Let’s shorten the conversionprocess by first cubing the relation between inches and centimeters:(1in) 3 = (2.54cm) 3 −→ 1in 3 = 16.39cm 3Now we can proceed with the conversion—watch the cancellations:1 ✚ gal1 × 3.785 ✓L1 ✚ gal× 1000✟✟ mL× 1✟✟ cm 31✓L 1✟mL ✟ ×1in316.39✟cm ✟3.785 × 1000= in 3 ≈ 231in 33 16.396
5. Don’t let the fact that these are compound units throw you off. All weare really converting is ft to m, and looking at the table we see that weneed to go from feet to inches to centimeters to meters:50ft1s × 12 in1ft × 2.54 ✟✟ cm1in× 1m100✟✟ cm50 × 12 × 2.54 m=100 s = 15.24m s6. Looking at the conversion table, we see that we need to convert from pintsto quarts to gallons to liters to milliliters.1pt1 × 1 qt2pt × 1 ✚ gal4qt × 3.785 ✓L1 ✚ gal× 1000mL1✓L=3.785 × 1000mL ≈ 473.1mL2 × 47
Page 3 and 4: we use the fact that 1ft=12in, and
Page 5: 6 Example ProblemsHere are some mor

Unit Conversions

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