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 review another example, click on Example.

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.

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