General strategy for converting units: QUESTION: Given: 1 inch is exactly equivalent to 2.54 cm, and 12 inches is exactly 1 foot. A measurement of 7.00 cm is equivalent to how many feet? A. 1.48 ft, B. 1.5 ft, C. 0.23 ft, D. 0.230 ft General strategy for converting units: (known amount) x (conversion factor) Conversion factor = ratio of equivalent amounts; set up so that original unit cancels out. Given that 1 inch is exactly equivalent to 2.54 cm, and 12 inches is exactly 1 foot. A measurement of 7.00 cm is equivalent to how many feet? PAUSE CLICK The general strategy for converting units is to multiply the known amount by a conversion factor. THe conversion factor is just the ratio of equivalent amounts. We need to set up the conversion factor so that the original unit cancels out. CLICK CONTINUED ON NEXT SLIDE

QUESTION: Given: 1 inch is exactly equivalent to 2.54 cm, and 12 inches is exactly 1 foot. A measurement of 7.0 cm is equivalent to how many feet? A. 1.48 ft, B. 1.5 ft, C. 0.23 ft, D. 0.230 ft 1 in. 1 ft 7.0 cm x x = 0.22966 ft  0.23 ft 2.54 cm 12 in. Since we are given that one inch is equivalent to 2.54 centimeters, we can write a conversion factor with 1 inch in the numerator and 2.54 centimeters in the denominator. HIGHLIGHT 1 in. / 2.54 cm Or we can write a conversion factor with 2.54 centimeters in the numerator and 1 inch in the denominator HIGHLIGHT 2.54 cm / 1 in. We can use these conversion factors to convert centimeters to inches, or inches to centimeters. CLICK Similarly, since 1 ft is equivalent to 12 inches, we can write a conversion factor with 12 inches in the numerator and 1 foot in the denominator. HIGHLIGHT 12 in. / 1 ft. or we can write a conversion factor with 1 foot in the numerator and 12 inches in the denominator. We can use these conversion factors to convert inches to feet, or feet to inches. The question is asking us to convert 7.0 centimeters to feet, and none of the conversion factors we have here allows us to do that. However, it should be easy to see that we can accomplish the conversion by first converting centimeters to inches. then convert the result, ...which is in inches..., to feet. So, here’s how it’s done. Start with the known measurement. 7.0 centimeters Multiply it by a conversion factor to convert centimeters to inches. CLICK CLICK CLICK THen multiply by a conversion factor to convert inches to feet. CLICK CLICK CLICK CLICK Punching all these numbers in a calculator gives us 0.22966 ft, which should be rounded off to only two significant figures. Therefore, the correct answer is C, 0.23 ft. We only keep two significant digits in the answer because the original measurement, 7.0 centimeters, has two significant figures. All the numbers in the conversion factors are exact and have no uncertainty. CLICK PAUSE END RECORDING cm  in. in.  cm in.  ft ft  in. 1 in. 2.54 cm 12 in. 1 ft 2.54 cm 1 in. 1 ft 12 in.

Video ID: 1A-5-2 © 2008, Project VALUE (Video Assessment Library for Undergraduate Education), Department of Physical Sciences Nicholls State University Author: Glenn V. Lo Narrator: Funded by Louisiana Board of Regents Contract No. LA-DL-SELECT-13-07/08