Units of Conversion: Linear Measure

Basic to the understanding of unit conversion is the understanding equivalence, the understanding of the multiplicative identity of 1, and how the two are related. For a review of these concepts, click on Review.

If you have forgotten how to manipulate fractions, visit Fractions for Adults on SOSMath for an in-depth review.

Review the following table (Webster's New World Dictionary, Second Edition, Simon and Schuster, 1982) of Standard Units of Conversion to see if you can create fractions that have a value of 1. You can click to examples following each table.

LinearMeasure

Example 4: Convert 100 meters to miles.

Solution.

Method 1: Convert meters to feet to miles in one step.

• Convert 100 meters to a fraction and multiply by 1 twice:

• Replace the first 1 by the fraction and the second 1 by the fraction

• Multiply the fractions:

• Look for the fractions whose values are 1 and rewrite the fraction as four fractions:

• 0.062136 x 1 x 1 x 1 mile = 0.062136 miles

• Note that his answer is not exact. It is an approximation because we rounded the answer to six places.

• When you were in high school, you probably took the original fraction and crossed out the meters and the feet. Most people do this without realizing that what they are doing is finding the fractions whose values are 1.

Method 2: Convert meters to decameters to hectometers to kilometers to miles.

• Convert 100 meters to a fraction and multiply by 1 four times.

• Multiply the numerators and multiply the denominators:

• Rewrite the numerator and denominator so that units stand alone.

• Rearrange numerator and denominator:

• Rewrite as the product of several fractions:

• Simply.0.0621 x 1 x 1 x 1 x 1 mile = 0.0621 miles

This answer does not match the answer we derived in Method 1 because of the way we rounded. Remember that both of the answers are approximations because of the rounding.

If you would like to practice some problems click on Problems.

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