The United States uses a variation of the Imperial system, known as the U.S. Customary Units, for its measurement values. However, most of the world uses the International System of Units, the modern iteration of the Metric system. The exam will likely provide some conversions and values for U.S. Customary Units measurements, but you are expected to know conversions for International System of Units measurements.

You are not expected to know conversions of measurements between the two systems, and you will be provided those conversions on the exam. Units of measurement for time are the same in both systems.

All of these conversions are ratios, meaning that for a certain amount of one measurement there is a certain amount of another measurement. Thus, conversions are the products of these ratios.

We can use a process called dimensional analysis to convert one unit to another.

**Dimensional Analysis**

Dimensional Analysis is a way to make unit conversion simple and organized. We simply multiply by proportions equal to 1 that represent the conversion factor until we reach our desired unit.

**Example**

Tim swims 624 inches in a race. How many feet did he swim?

These are important conversions of length:

Here is one length conversion problem:

These are important conversions of volume:

Here is one volume conversion problem:

These are important conversions of mass:

Here is one mass conversion problem:

These are important conversions of time:

Here is one time conversion problem:

Now that you’ve seen different units of measurement and sample conversions, think again about how to eliminate units to arrive at a final desired unit. One important thing to consider is that a variety of steps can be used to arrive at the unit you want.

For example, in the volume conversion problem, you converted 4 gallons to fluid ounces by converting to quarts, then pints, then cups, then finally fluid ounces. However, if you knew that 1 quart is 32 fluid ounces, you could skip two of those steps. Instead, you could surmise that 4 gallons is 16 quarts, thus (16)(32) = 512.

This is just one case, but conversions can be done in as many or as few steps as you need. What’s important is that the ratios remain intact.

**Practice Problems**

- Convert 40,000 seconds into hours.
- Convert 4 cubic meters into milliliters.
- Convert 7 miles into yards.
- Convert 52,789,333 millimeters into kilometers.
- Convert 20 gallons into cups.
- Convert 18 tons into ounces.
- An Olympic swimmer swims at a rate of 10 meters per second. How fast is the swimmer swimming in kilometers per hour?
- 30
*km/h* - 32
*km/h* - 34
*km/h* - 36
*km/h*

- 30

**Answers**

- 11.11 hours
- 4,000,000 mL
- 12,320 yds
- 52.789 km
- 320 cups
- 576,000 oz
- 36 km/hr

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