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SAT Unit Conversion Questions

Conversion questions on the SAT usually hide inside a rate problem: something moves at a given speed in one unit system and the answer is wanted in another. The arithmetic is easy. The failure point is setting up the factors so the unwanted units actually cancel instead of piling up.

The rule

Arrange each conversion factor so the unit you want to remove appears once on top and once on the bottom.

Write every quantity as a fraction with units attached, then multiply by conversion fractions arranged so the unit you want gone appears once on top and once on the bottom. To convert 90 minutes to hours, multiply 90 minutes by 1 hour over 60 minutes. The word minutes appears on top and on the bottom, so it cancels, leaving 90 over 60, which is 1.5 hours.

Getting the factor upside down is the whole trap. If you had multiplied by 60 minutes over 1 hour, the units would have been minutes times minutes over hours, which is meaningless, and the answer 5,400 would be off by a factor of 3,600. You do not need to remember which way the factor goes. You only need to look at which unit you want to cancel and place it opposite.

Chained conversions go in one line. To convert 20 meters per second into meters per hour, multiply by 60 seconds over 1 minute and then by 60 minutes over 1 hour. Seconds cancel, then minutes cancel, leaving 20 times 3,600, which is 72,000 meters per hour. Write all the factors first and confirm the cancellations visually before you multiply anything.

Squared and cubed units need the factor applied that many times. There are 3 feet in a yard, but there are 9 square feet in a square yard, because both the length and the width convert. Similarly there are 27 cubic feet in a cubic yard. If a question converts an area or a volume, square or cube the linear conversion factor rather than using it once.

Rates with two different units in the same problem are where conversions hide. A question giving a cost per gallon and a consumption in liters, or a speed in miles per hour and a time in minutes, is asking you to convert before combining. Scan for two units measuring the same kind of thing and convert one to match the other before you set up any proportion.

The trap

Flipping a conversion factor, so the unit you meant to cancel gets multiplied instead and the answer is off by the square of the factor.

Try it

Try one
Real question

In a class, the ratio of boys to girls is 1:4. If there are 25 students in total, how many are boys?

A bag contains only red and green tokens, and the ratio of red to green is 4 to 7. After 15 more green tokens are added, the ratio of red to green becomes 2 to 5. How many red tokens are in the bag?

  • A) 20 ✓
  • B) 28
  • C) 35
  • D) 40

Why: Let red = 4k and green = 7k. Adding 15 green gives 4k/(7k + 15) = 2/5. Cross-multiply: 20k = 14k + 30, so 6k = 30 and k = 5. Red = 4(5) = 20, with green 35 before the change and 50 after, and 20/50 = 2/5. 35 is that green count before the tokens were added, not the red count. 28 would make green 49, and after the 15 are added 28/64 is not 2/5. 40 would make green 70, and 40/85 is not 2/5 either.

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Questions students ask

Does the SAT give me the conversion factors?

Conversions between different measurement systems are provided in the question when they are needed. You are expected to know common ones within a system, such as 60 seconds in a minute, 12 inches in a foot, and 100 centimeters in a meter.

How do I convert square or cubic units?

Apply the linear factor once for each dimension. Since 1 foot is 12 inches, 1 square foot is 12 times 12, or 144 square inches, and 1 cubic foot is 12 cubed, or 1,728 cubic inches. Using the linear factor once on an area is a common source of wrong answers.

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