# 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 2: Convert 4.6 kilometers to miles.

Solution:

• Write 4.6 kilometers as a fraction by dividing it by 1:
• Multiply the fraction by 1: 1.
• The Webster Dictionary states that there are approximately 0.621 miles in 1 kilometer; therefore the fraction is equivalent to 1 because the numerator and the denominator measure the same length.

• Rewrite the expression 1 with the 1 converted to the fraction :

• Rewrite 4.6 kilometers as and 0.621 miles as :

• Multiply the two fractions:
• Rearrange the numerator:
• Write the above fraction as two fractions:
• Replace the fraction by 1:

• Simplify: 2.8566 miles

If you would like to review another example, click on Example.

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

[Units of Conversion]