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**

**Problem 4: **Convert 86 square decimeters to square
hectometers

**Answer:** 8.6 x 10 ** square hectometer**

**Solution**: Look for a series of links from square decimeters to
square hectometers.

- From the table you can see that there are links from square decimeters to square meters to square decameters to square hectometers.
- According to the table, 1 square meter is equivalent to 100 square
decimeters.
Therefore, the fraction is equivalent to 1.

- According to the table, 1 square decameter is equivalent to 100
square meters.
Therefore, the fraction is equivalent to 1.

- According to the table, 1 square hectometer is equivalent to 100
square decameters.
Therefore, the fraction is equivalent to 1.

Rewrite 86 square decimeters as a fraction and multiply the fraction by 1 three 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: 8.6 x 10 square hectometers or 0.000086 square hectometers

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

= 8.6 x 10 square hectometer.

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

If you would like to go to 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 22:51:39 MDT 1997*

Contact us

Math Medics, LLC. - P.O. Box 12395 - El Paso TX 79913 - USA

users online during the last hour