Compute percent of a quantity and convert among percent/decimal/fraction. | Percentages | SAT Math

Core Idea

Percent, decimal, and fraction are three outfits for the same number. Converting between them is just moving the decimal point or simplifying a fraction over 100.

Understanding

To convert a percent to a decimal, divide by 100 (move the decimal two places left). To go from a decimal back to a percent, multiply by 100. To write a percent as a fraction, put it over 100 and reduce.

$45 % = 45100 = 0.45$

Finding a percent of a quantity means multiplying. "What is 30% of 250?" becomes $0.30 \times 250 = 75$ . That's it.

The reverse question — "60 is what percent of 80?" — is a division problem:

$6080 = 0.75 = 75 %$

The part you're looking for always goes in the numerator; the whole (the base) goes in the denominator. Mixing up which is which is the single most common mistake on these problems.

Fractions with "nicer" denominators are worth memorizing as percents: $14 = 25 %$ , $13 \approx 33.3 %$ , $15 = 20 %$ , $38 = 37.5 %$ . On a timed test, instant recall beats recalculating.

Step by Step

Identify what role each number plays: is it the part, the whole, or the percent?
Convert the percent to a decimal (divide by 100) or a fraction as needed.
Set up the relationship: Part = Percent × Whole.
Solve for the unknown quantity.

Misconceptions

Dividing by the part instead of the whole when finding what percent one number is of another — e.g., writing $8060$ instead of $6080$ .
Forgetting to move the decimal two places when converting between percent and decimal form (writing 0.045 instead of 0.45 for 45%).
Treating the percent number as though it's already a decimal — multiplying by 45 instead of 0.45 when finding 45% of something.

Question

Worked Example

A store has 240 items in stock. If 35% of the items are on sale, how many items are NOT on sale?

Select an answer to see the explanation