Percents
Convert fractions to percents and take common percents of amounts.
Best in your head · no pen, no calculator why?
Opens at level 8. You're level 1. You can read and practice here now.
the idea
Percent means per hundred. 25% is 25 out of 100, which is the fraction 1/4 and the decimal 0.25: three ways to write one amount.
more of the idea
To change a percent to a decimal, divide by 100, which moves the point two places left. To go the other way, multiply by 100. A few pairs are worth knowing by heart: 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5%, and 1/10 = 10%.
To find a percent of an amount, build it from pieces you can work out in your head.
techniques
Move the point two places
- Percent to decimal: divide by 100. The point moves two places left, so 60% is 0.6.
- Decimal to percent: multiply by 100. The point moves two places right, so 0.375 is 37.5%.
- Add zeros if you run out of digits: 5% is 0.05.
Write 12.5% as a decimal.
- Divide by 100: move the point two places left.
- 12.5 becomes 0.125.
Answer: 0.125
Start from one part
- Find one part as a percent: 100 ÷ 8 = 12.5, so 1/8 = 12.5%.
- Multiply by the top number.
- Learn the halves, quarters, fifths and tenths by heart. Eighths are half of quarters.
Write 3/5 as a percent.
- 1/5 = 20%.
- 3/5 = 3 × 20% = 60%.
Answer: 60%
Build from 10%, 5% and 1%
- 10% is the amount ÷ 10, and 1% is the amount ÷ 100.
- 5% is half of 10%. 20% is double 10%, and 30% is three times it.
- 15% = 10% + 5%, and 35% = 25% + 10%.
- 25% is a quarter, 12.5% is an eighth, and 75% is the whole minus a quarter.
What is 35% of 60?
- 25% is a quarter: 60 ÷ 4 = 15.
- 10% is 60 ÷ 10 = 6.
- 15 + 6 = 21.
Answer: 21
watch out for
- Moving the point only one place. 60% is 0.6, not 6, because percent means per hundred.
- Keeping the decimal and adding a percent sign. 0.375 is 37.5%, not 0.375%.
- Treating 5% as a fifth. A fifth is 20%; 5% is half of 10%.
- Stopping at 10% when the question asks for 15%. Add the 5% as well.
practice
New here? Start the four-problem warm-up. No sign-up.
Percent to decimal
worked example
Write 5% as a decimal.
- Percent means per hundred: 5 ÷ 100 = 0.05.
Answer: 0.05
Fraction to percent
worked example
Write 0.9 as a percent.
- Multiply by 100: 0.9 × 100 = 90, so 0.9 = 90%.
Answer: 90%
1%, 5%, 10%
worked example
What is 10% of 1,500?
- 10% is one tenth: 1,500 ÷ 10 = 150.
Answer: 150
Build a percent
worked example
What is 75% of 164?
- 75% is the whole minus one quarter: 164 − 41 = 123.
Answer: 123