


Introduction It is often necessary to convert a value from one system of units into another. Sometimes the unit scale needs to be moved up or down in order to give the outside observer the proper perspective. For instance, if I tell a person that I live 2,600,000 inches from Baton Rouge, they may realize I live far away, yet cannot perceive just how far. If I say, however, that I live 41 miles from Baton Rouge, they can much better visualize the scale. Unit conversion may also be necessitated when quantities measured in one system are combined, then reported in a standardized unit which practioners use on a regular basis. To properly convert units, we employ dimensional analysis. We all have an innate ability to perform dimensional analysis, so we will investigate a manner to systematize this. Example 1: Simple Conversion FactorsLet's ssy for instance that you purchase donuts at a bakery and buy 3 dozen, it is apparent that you bought 36 donuts. If you want one donut for each of 24 people, you would purchase 2 dozen. In your mind, you were able to make the conversion from the unit of dozen into individual donuts and vice versa. You were also naturally know that you multiply by 12 in the former case, and divide by 12 in the latter. To systematize this process, we will use a conversion factor The conversion factor is placed in the form of a fraction, arranged so that the unit to be changed is in the denominator and the unit desired is in the numerator. The units are arranged to algebraically cancel, and this automatically indicates the operation of the numeric values :
Example 2: MultiDimensional Conversion
If one wishes to convert this quantity to square feet, you must apply the conversion factor of 1 yd = 3 ft twice:
Example 3: Fractional Unit Conversion
In the following example, the density of a substance is converted from units of grams/milliliter into pounds/inch^{3}. Notice that this example applies the conversion factor 1 in = 2.54 cm three times:
Unit Conversion and Significant Figures



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