Question type

Unit conversion and rates on the SAT

Multiply by conversion factors written as fractions equal to 1, arranged so the units cancel: $25 \frac{m}{s} \times \frac{3600 s}{1 h} \times \frac{1 km}{1000 m} = 90 \frac{km}{h}$ . For squared or cubed units, square or cube the factor. The SAT states every factor except time.

These questions convert a rate from one set of units to another, such as feet per second to miles per hour, or chain a conversion through a scale or an intermediate rate.

It appeared on two of the five official practice tests we analysed. The SAT always states the conversion factors it expects you to use, in the text or in parentheses, except time: you are expected to know 60 seconds, 60 minutes and 24 hours.

On 2 of 5 official practice tests
Desmos helps

Why students miss it

Multiplying where you should divide. Writing the factors as fractions and cancelling units prevents it.

Converting one unit of a rate and forgetting the other: meters per second to kilometers per hour needs both meters and seconds converted.

Squared units. Converting square feet to square inches multiplies by $1 2^{2} = 144$ , not 12.

How to spot it

A rate with "per": meters per second, pages per minute, dollars per liter.
A conversion factor in parentheses: (1 kilometer = 1,000 meters).
A map scale or an answer in a different unit from the data.

The method

Cancel the units

Write the quantity with its units, then multiply by factors equal to 1.

Unit to cancel is on top: put it on the bottom of the next factor.
Unit to cancel is on the bottom: put it on top of the next factor.
Squared or cubed unit: square or cube the factor.

With Desmos

Desmos handles the arithmetic once the factors are arranged.

Type 25*3600/1000 and read 90 km per hour.
Keep the factors in one line so nothing is rounded halfway.

Two real questions

From the 1500prep bank, the way the app shows them. Answer first, then open the explanation.

1Question 1 of 2#552Data

On a map, a distance of 1 inch represents an actual distance of 2.5 miles. Two landmarks are 6.4 inches apart on the map. If 1 mile is equal to 5,280 feet, what is the actual distance between the landmarks, in feet?

Pick an answer, then check it.

Show the answer and explanation

Convert in two steps: map inches → miles → feet.

6.4

inches

\times 2.5

miles per inch

= 16

miles. Then

16 \times 5, 280 = 84, 480

feet. Keeping the units attached (

\frac{2.5 mi}{1 in}

\frac{5 , 280 ft}{1 mi}

) makes sure each factor lands in the right place.

2Question 2 of 2#547Data

A train travels at a constant speed of 25 meters per second. What is this speed, in kilometers per hour? (1 kilometer = 1,000 meters)

Pick an answer, then check it.

Show the answer and explanation

Convert both units in one chain:

\frac{25 m}{1 s} \times \frac{3600 s}{1 h} \times \frac{1 km}{1000 m} = \frac{25 \times 3600}{1000} = 90

kilometers per hour.

Questions students ask

Does the SAT give you conversion factors?

Yes, for everything except time. Factors like 1 kilometer = 1,000 meters or 1 mile = 5,280 feet are stated in the question; seconds, minutes, hours and days are assumed known.

How do you convert meters per second to kilometers per hour?

Multiply by 3,600 (seconds in an hour) and divide by 1,000 (meters in a kilometer): in effect, multiply by 3.6. 25 m/s is 90 km/h.

Practise this type until it is automatic

Five more unit-conversion questions, checked instantly, with every wrong choice explained. Free, no card.

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