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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.)

Practice: Convert units in multiple steps
The Kentucky Derby is a horse race run over a distance of 10 furlongs. The fastest Derby winners complete the race in about 2 minutes. To the nearest tenth of a mile per hour, how fast must a horse run to complete the Derby in 2 minutes? (1 mile equals, 8 furlongs)

## Want to join the conversation?

• kindly can someone tell me what the unit equivalencies for time and for metric units of mass, distance, and volume are please?
• The metric system is a system of measurement that uses the meter, liter, and gram as base units of length (distance), capacity (volume), and weight (mass) respectively. Hopes this helps a little <33
(1 vote)
• If it's okay, could someone pls let me know what all units we need to know i.e. the ones that won't be included in the question?
• Here's a list of units that aren't commonly given to you, as most American students would probably have these memorized:
1 foot = 12 inches
1 yard = 3 feet
1 dollar = 100 pennies, 1 quarter = 25 pennies, 1 dime = 10 pennies, 1 nickel = 5 pennies
1 minute = 60 seconds
1 hour = 60 minutes
1 day = 24 hours
In addition, knowing the metric prefixes for units might help. I don't remember seeing a question that asks you to convert between units of capacity (like pints and gallons) without giving you the conversion factor, but you might find worth out of memorizing those too.
• shouldn't the density be 2.6 in pursuing the mass of the marble slab?
• Yes, the density should be and is 2.6 grams per cubic centimeter. Density is in units of mass per unit volume, so to get the mass from the density and volume, we multiply density and volume together.
The volume of the slab is 40,000 cubic centimeters. Multiplying this by density gives you D) 104,000 grams.
• I have practiced a lot of sat practice papers from crackSAT but I found out that some of the questions do not have a conversion factor stated; for example: (1 foot = 12 inches) and so. There were some unknown units namely, dimes, nickels, and 1 ton being 2000 pounds (I thought 1 ton was 1000 kgs up until now lmao) and others as well. While practicing, I googled the unit conversion factor but what if such situation arise in the real exam. And how likely is this type of scenario to occur?
• On the real SAT, there should be no units that you would have a huge amount of trouble with. I think the following units might have a chance to be presented to you without a conversion factor, but all else (including money) should be:
Length: inches, feet, yards, miles
Capacity: cups, pints, quarts, gallons
Weight: ounces, pounds, tons
• Could you explain to me this last question pls About the Kentucky Derby?
(1 vote)
• The question wants you to give a final answer in miles per hour. This means we have to somehow convert our units so that we end up with everything canceling out except miles in the numerator and hours in the denominator. Using the same process in the rest of the article, all we have to do is set up a bunch of ratios to multiply with each other given the statements in the problem:
10 furlongs * (1 mile / 8 furlongs) = 1.25 mi
To go from miles to miles per hour, we just divide by our time (in hours):
1.25 mi / (2 min * (1 hour / 60 min)) = 37.5 mph