# Units of Conversion: Square (Area) Measure - Problem 4

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.

[Units of Conversion]