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**.

You will also need to multiply and reduce fractions. If you have forgotten
how to manipulate fractions, visit **Fractions for Adults** on SOSMath
for an in-depth review.

Review the following table 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.

**Cubic Measure**

**Example 3****: Convert 31.5 cubic centimeters
to cubic feet.**

**Answer:**

Note: One cubic centimeter means 1 centimeter 1 centimeter 1 centimeter. One cubic centimeter also means 1 centimeter^{3}.

- Write 31.5 cubic centimeters as a fraction.
- You can see from the above table that there is a link between centimeters and inches and between inches and feet.
- Since 1,000 cubic centimeters is equivalent to 61.023 cubic
inches, you can write
the fraction
as an equivalent form of 1.

- Since 1,728 cubic inches is equivalent to 1 cubic foot, you
can write the
fraction
as an equivalent form of 1.

- Note that is
equivalent to
- Write as
- Multiply the fractions.
- Rewrite the numerator and denominator.
- Rearrange the numerator and denominator.
- At this point, you can cancel the centimeters and the inches.The following steps will remind you why you can cancel these terms.
- Rewrite the above fraction as four fractions so that two of
the fractions have an
equivalent value of 1.
- The above can now be written
- It can be further simplified to 0.001112 x 1 cubic foot or 0.001112 cubic foot.

At this point, you might argue that what we illustrated is "over kill" of a simple problem.

Keep in mind, that this site is a tutoring/review site. A shorter version of the same problem is shown below.

- Start with
- Cancel the centimeters and the inches to have
- This in turn can be simplified to 0.001112 cubic foot.

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.**

Do you need more help? Please post your question on our S.O.S. Mathematics CyberBoard.

*
Sep 26 1997*

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