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## SAT

### Course: SAT>Unit 6

Lesson 5: Problem Solving and Data Analysis: lessons by skill

# Units | Lesson

## What is unit conversion, and how frequently does it appear on the test?

We use units—inches, centimeters, and miles, etc.—to measure quantities like time, mass, and distance. But we can use a variety of units to measure the same thing. For example, inches, centimeters, and miles are all measures of distance.
Unit conversion lets us change the units in which a measurement is given.
In this lesson, we'll practice converting between units in a variety of scenarios.
On your official SAT, you'll likely see 2 to 3 questions that require you to make unit conversions. You may also need to deal with units in other types of questions.
Note: You'll be expected to know the unit equivalencies for time and for metric units of mass, distance, and volume. All other unit equivalencies will be provided for you.
You can learn anything. Let's do this!

## How do we convert between units?

Measurement word problem: blood driveSee video transcript

### Applying unit to unit ratios

On the SAT, the relationships between units will be provided to you in the form of a equivalency (e.g., 1 foot equals, 12 inches).
It's useful to think of this equivalency as a ratio (e.g., 1 foot : 12 inches or start fraction, 1, start text, space, f, o, o, t, end text, divided by, 12, start text, space, i, n, c, h, e, s, end text, end fraction). You'll then multiply the initial measurement by that ratio to convert from one unit to the other.
Note: It's important to remember that every unit (besides the unit you're looking for) should appear once in the numerator and once in the denominator. That way, all other units can be cancelled out!
For example, to convert 2, comma, 000 grams to kilograms:
2, comma, 000, start cancel, start color #7854ab, start text, g, r, a, m, s, end text, end color #7854ab, end cancel, dot, start fraction, 1, start text, space, k, i, l, o, g, r, a, m, end text, divided by, 1, comma, 000, start cancel, start color #7854ab, start text, g, r, a, m, s, end text, end color #7854ab, end cancel, end fraction, equals, 2, start text, space, k, i, l, o, g, r, a, m, s, end text
2, comma, 000 grams is equal to 2 kilograms.
As long as we set up our ratios correctly, this process will work no matter how many conversion steps we need.

Example:
\begin{aligned} &1\,\text{yard}=3\,\text{feet} \\ \\ &12\,\text{inches}=1\,\text{foot} \end{aligned}
How many inches are in one yard?

### Converting units within rates

You may be asked to convert units that appear within a rate. This can feel tricky, since rates are the quotient of two different units, e.g., start fraction, start text, m, i, l, e, s, end text, divided by, start text, h, o, u, r, end text, end fraction.
But don't worry! The same rules apply as with any unit conversion: just make sure that the units you want to eliminate appear in both the numerator and denominator of your conversion operation.

Example: A whitetail deer can run at a maximum speed of 30 miles per hour. What is a whitetail deer's maximum speed in feet per minute? (1 mile equals, 5, comma, 280 feet)

### Try it!

Try: Set up a unit conversion
You're provided a measurement in cubic centimeters. You're told that 1 cubic centimeter is equal to 1 milliliter (1 cubic centimeter equals, 1 milliliter) and that 1 fluid ounce is equal to about 29, point, 57 milliliters (1 ounce approximately equals, 29, point, 57 milliliters).
Which of the following operations would convert the initial measurement (x) into fluid ounces?

Practice: convert units in one step
Ranjit wants to measure the length of a table, but has no ruler or tape measure. Using what he has at hand, he finds that the table is about as long as 6 unsharpened pencils laid tip to tip. If each unsharpened pencil measures 18 centimeters in length, what is the length of the table, in centimeters?

Practice: Use a rate to convert units
A marble slab in the shape of a right rectangular prism has dimensions of 100 centimeters by 80 centimeters by 5 centimeters. The slab has a density of 2, point, 6 grams per cubic centimeter. What is the mass of the marble slab, in grams? (Density is mass per unit volume.)