Fractions, Decimals and Percentages

In short: Fractions, decimals and percentages are three ways to write the same amount, and percent means out of 100, so $35% = \frac{35}{100} = 0.35$ . To find a percentage of an amount, build it from 10%, 5% and 1%.

Before you start

A fraction like $\frac{3}{4}$ means 3 parts out of 4 equal parts. The top is the numerator and the bottom is the denominator.
Equivalent fractions: multiply or divide top and bottom by the same number, such as $\frac{1}{5} = \frac{20}{100}$ .
Decimal place value: $0.35$ is 35 hundredths.

Percent means "out of 100"

The sign $%$ means per cent, which is "out of 100". So $35% = \frac{35}{100} = 0.35$ .

Key ideaConverting

From	To	How
percentage	fraction	write over 100 and simplify: $60% = \frac{60}{100} = \frac{3}{5}$
percentage	decimal	divide by 100: $5% = 0.05$
decimal	percentage	multiply by 100: $0.8 = 80%$
fraction	percentage	make the bottom 100, or multiply by $100%$ : $\frac{1}{4} = \frac{25}{100} = 25%$

Facts worth knowing by heart

Fraction	Decimal	Percentage
$\frac{1}{2}$	$0.5$	$50%$
$\frac{1}{4}$	$0.25$	$25%$
$\frac{3}{4}$	$0.75$	$75%$
$\frac{1}{5}$	$0.2$	$20%$
$\frac{1}{10}$	$0.1$	$10%$
$\frac{1}{20}$	$0.05$	$5%$
$\frac{1}{100}$	$0.01$	$1%$
$\frac{1}{3}$	$0.333 \dots$	$33 \frac{1}{3} %$

A whole is $100%$ , so $65% + 35% = 100% = 1$ .

Finding a percentage of an amount

Going backwards

If you know the part, you can find the whole.

Fractions, decimals, percentages

Percent

Out of 100
$35% = 0.35$

Convert

% to decimal: ÷ 100
Decimal to %: x 100
Fraction: make the bottom 100

Percent of an amount

10%: ÷ 10
5%: ÷ 20
Add pieces

Backwards

5% is 12, so the whole is 240

Quick summary

Percent means out of 100: $35% = \frac{35}{100} = 0.35$ .
Percentage to decimal: divide by 100. Decimal to percentage: multiply by 100.
Learn the common ones: $\frac{1}{2} = 50%$ , $\frac{1}{4} = 25%$ , $\frac{1}{5} = 20%$ , $\frac{1}{20} = 5%$ .
For a percentage of an amount, build it from $10%$ , $5%$ and $1%$ .
$5%$ of an amount is the amount divided by 20.
To find the whole from a part, work backwards.

Quiz

13 questions with instant marking. It is free, and your scores are saved to your account so you can carry on from any device.

Turn on JavaScript to sign in and take the quiz.

Try 3 questions now

$0.05 =$
1. A $50%$
2. B $5%$
3. C $0.5%$
4. D $0.05%$
Show answer
B: $5%$
Multiply by 100: $0.05 \times 100 = 5$ .
$20% = \frac{□}{5}$ . What is in the box?
1. A 1
2. B 2
3. C 4
4. D 20
Show answer
A: 1
$20% = \frac{20}{100} = \frac{1}{5}$ .
What is $10%$ of 340?
1. A 3.4
2. B 34
3. C 340
4. D 30
Show answer
B: 34
Divide by 10: 34.