# Standard Measurement Conversions

Although much of the world uses the metric measurement system, the United States uses U.S. Customary Measurements, which we often call the standard measurement system.

Conversions from unit to unit is fairly easy, using proportions.

First, students need to memorize (or have reference to) the conversion ratios (below, find a link for a PDF conversion card that students can use for reference).

 Length Weight Liquid Volume 1 foot = 12 inches 1 pound = 16 ounces 1 cup = 8 fluid ounces 1 yard = 3 feet 1 ton = 2000 pounds 1 pint = 2 cups 36 inches 32,000 ounces 16 fluid ounces 1 mile = 1,760 yards 1 quart = 2 pints 5,280 feet 4 cups 63,360 inches 32 fluid ounces 1 gallon = 4 quarts 8 pints 16 cups 128 fluid ounces

Once students know the conversion ratios, they can use proportions to convert units.

Example:

Jason needs to buy 17 yards of tubing for a science project.  The tubing is sold by the foot.  How many feet of tubing does he need?

1. Find the conversion ratio between feet and yards: $\dfrac{1 \text{ yard}}{3 \text{ feet}}$
2. Create a proportion that sets the conversion ratio next to a new fraction, that contains the known amount, and the unknown amount as $x$. Remember to match up the units.  The units on the top and bottom of the fractions should match. $\dfrac{1 \text{ yard}}{3 \text{ feet}}=\dfrac{17 \text{ yards}}{x \text{ feet}}$
3. Cross multiply to solve for x. \eqalign{\dfrac{1 \text{ yard}}{3 \text{ feet}}&=\dfrac{17 \text{ yards}}{x \text{ feet}}\\1 \times x &= 3 \times 17\\x&=51}

Jason needs 51 feet of tubing.

Alternate Method:

Once you know the conversion ratios, you can just multiply to convert to smaller units or divide to convert to larger units.

Example:

Jason needs to buy 17 yards of tubing for a science project.  The tubing is sold by the foot.  How many feet of tubing does he need?

$17 \times 3 \text{ feet} = 51 \text{ yards}$

This method is more efficient.  BUT, students often get confused about whether they should multiply or divide.  Lining up the labels in the proportions helps to guide students to the correct operation.  Plus, setting up this proportion helps students prepare for advanced conversions when they need to use multiple conversion ratios.