# Units of Conversion: Square (Area) Measure - Example 3

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 3: Convert 6,000 square decameters to sections.

Solution: Look for a series of links from decameter to section.

• From the table you can see that there are links from decameters to yards to feet to miles to acres to sections.

• According to the table, 1 square decameter is equivalent to 119.6 square yards.

Therefore the fraction is equivalent to 1.

• According to the table, 1 square yard is equivalent to 9 square feet. Therefore, the fraction is equivalent to 1.

• According to the table, there are 5,280 feet in one mile, and 5,280 x 5,280 = 27,878,400 square feet in one square mile.Therefore, the fraction is equivalent to 1.

• According to the table, 1 square mile is equivalent to 1 section. Therefore the fraction is equivalent to 1.

• Rewrite 6,000 square decameters as a fraction and multiply the fraction by 1 four times.

• Convert the above four 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: 0.231663 1 1 1 1 1 section = 0.231663 section

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 equation

= 0.231663 section

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.

[Units of Conversion]