Basic to the understanding of unit conversion is the understanding of
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.

**Square Measure**

**Example 4:** Convert 500 hectares to square feet.

**Solution:** Look for a series of links from hectares to square
feet.

- From the table you can see that there are links from hectares to
acres to square feet.
- According to the table, 1 hectare is equivalent to 247.1
acres.
Therefore, the fraction is equivalent to 1.

- According to the table, 1 acre is equivalent to 43,560 square feet. Therefore, the fraction is equivalent to 1.

- Rewrite 500 hectares as a fraction and multiply the fraction by 1 two
times.

- Convert the above 1's to equivalent fractions.

- Multiply the numerators and multiply the denominators:

- Rewrite the fraction so that the units stand alone:

- Rearrange the numerator and the denominator:

- Rewrite as several fractions where most fractions have an equivalent
value of 1:

- Simplify: 5,381,838,000 1 1 1 square foot = 5,381,838,000 square feet

As you work more and more of this conversion problems, you can leave out a lot of steps and simply "cross out" similar units. In the original set-up

, you would simply cross out common units and go straight to the expression = 5,381,838,000 square feet

Just be sure that you remember why you are allowed to do the cancelling.

If you would like to work some problems click on *Problems.*

If you would like to go back to the table of contents, click on *Table of Contents**.*

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

*
Sun Aug 10 21:07:12 MDT 1997*

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