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Unformatted text preview: What is a conversion factor? June 13, 2011. Revised, June 18, 2011. Suppose there are two units of measurement at handinches and centimeters, say. Suppose we know the measure of an object with respect to one unit and we wish to compute the measure with respect to the other. We can achieve this by multiplying by the an appropriate conversion factor . For example, there are (by international agreement) exactly 2 . 54 centimeters in one inch, and therefore, the conversion factor that changes a number of inches to the number of centimeters that spans the same length as the inches is 2 . 54. If a piece of wire is carefully cut to exactly 69.5 inches, then its length in centimeters is 2 . 54 69 . 5 = 176 . 53. It is typical to think of the 2.54 as a rate, and to give it the label centimeters per inch. If an object is measured in inchesproducing the number n and is also measured in centimetersproducing the number m then m/n = 2 . 54. It does not matter how big or small the objects are. If we measure in both ways over and over, then as long as the measurements are accurate, we always get 2 . 54. Sources of confusion When working with conversion factors, it is easy to get confused. The reason seems to be related to the difficulty that some peoplemyself includedhave in translating certain kinds of statements into equations. For example: 1) Platos Trail Mix has 10 raisins for every 3 nuts. In a certain bag of Platos Trail Mix, the number of raisins is R and the number of nuts is N . Which is correct? a) 10 R = 3 N b) 3 R = 10 N 2) On June 18, 2011, the currency exchange rate was 1 euro = 1.4315 US dollars. If I had D dollars on that day, then what equation should I use to find out the number E of euros that my fortune was then worth? a) D = 1 . 4315 E b) E = 1 . 4315 D There are several possible sources of confusion: 1) If we pair the words with the most-closely-related symbols, then the order of the words in the statement, Ten raisins for every three nuts, is the same as the...
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- Summer '11