Fractions, Decimals and Percents — AP® Statistics Notes

The first numbers you compute from data are parts of a whole: how many students in a group out of how many in all. This page is the arithmetic behind them: fractions, decimals and percents, and how to choose the right whole.

A part over its whole

A part of a whole is a division:

$\frac{\text{part}}{\text{whole}}$

The answer is always between 0 and 1, because the part sits inside the whole. If you get a number bigger than 1, you have the fraction upside down.

Twenty-four boxes in a row, 18 shaded in plum, above a scale from 0 to 1 marked every 0.25. A dashed line at 0.75 marks where the shaded part ends. The caption reads: part over whole, 18 over 24, equals 0.75, equals 75%. — **Figure 1.** 18 of 24 boxes are shaded: $\frac{18}{24} = 0.75$ of the bar. LevlPrep original diagram.

Part, whole, decimal, percent. In a reading group, 18 of the 24 students finished the book.

The whole: the 24 students in the group. The part: the 18 who finished.

Decimal: $\frac{18}{24} = 0.75$ .

Percent: $0.75 \times 100 = 75\%$ .

In words: 75% of the reading group finished the book.

Decimals and percents

A percent is "out of 100". To turn a decimal into a percent, multiply by 100 (move the decimal point two places right). To turn a percent into a decimal, divide by 100.

Fraction	Decimal	Percent
$\frac{1}{4}$	0.25	25%
$\frac{3}{8}$	0.375	37.5%
$\frac{2}{25}$	0.08	8%
$\frac{2}{3}$	0.6667	66.7% (rounded)

Watch small percents: 8% is 0.08, not 0.8. And to find a percent of a number, multiply by the decimal: 45% of 300 is $0.45 \times 300 = 135$ .

Which whole?

The hardest part is usually picking the whole. Read the question for the word "of": the group after it is the whole.

Choose the whole. Of 60 seniors, 24 play a school sport, and 9 of those play two sports. What part of the sport players play two sports?

"Of the sport players": the whole is the 24 players, not the 60 seniors.

$\frac{9}{24} = 0.375$ , so 37.5% of the sport players play two sports.

The other question, "what part of all seniors play two sports?", has whole 60: $\frac{9}{60} = 0.15$ . Same part, different whole, different answer.

Compare parts, not counts

School A has 18 walkers out of 30 students, and school B has 25 out of 50. School B has more walkers, but it is also bigger. Divide each part by its own whole: $\frac{18}{30} = 0.60$ and $\frac{25}{50} = 0.50$ . A larger part of school A walks. Whenever groups have different sizes, compare decimals or percents.