# 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.

If you would like to go back to the table of contents, click on Main Menu.

[Units of Conversion]

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Author: Nancy Marcus
Fri Aug 2 12:03:12 MDT 1996

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