Units of Conversion: Square (Area) Measure - Example 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

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.

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