Maths
What is a percentage?
Quick answer
A percentage is a number out of 100, written with the sign %. So 25% means 25 out of every 100, which is the same as one quarter.
In one sentence
A percentage tells you how many out of 100, so 40% means 40 out of every 100.
Explained
Per cent comes from Latin and means "for each hundred". The sign % stands for "out of 100". If 100 children take a spelling test and 62 get full marks, 62% got full marks.
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Percentages are useful because they let you compare things fairly. Scoring 18 out of 20 and 42 out of 50 is hard to compare. As percentages, they are 90% and 84%, so the first score is better.
A few percentages are worth knowing by heart, because they match simple fractions and decimals:
| Percentage | Fraction | Decimal |
|---|---|---|
| 100% | 1 whole | 1 |
| 50% | ½ | 0.5 |
| 25% | ¼ | 0.25 |
| 10% | 1/10 | 0.1 |
| 1% | 1/100 | 0.01 |
To find a percentage of an amount in your head, start from 10% (divide by 10) and build up. For 35% of 80: 10% is 8, so 30% is 24, and 5% is half of 8, which is 4. Total: 28.
With a calculator, change the percentage to a decimal and multiply: 35% of 80 = 0.35 × 80 = 28.
To turn a score into a percentage, divide and multiply by 100. 17 out of 25 is 17 ÷ 25 = 0.68, which is 68%.
Examples
- 25% of 36 = ¼ of 36 = 9
- 1% of 300 = 3, so 7% of 300 = 21
- 20% off a $45 game: 10% is $4.50, 20% is $9, so it costs $36
- 12 out of 40 = 12 ÷ 40 = 0.3 = 30%
- 150% of 20 = 30 (percentages can go over 100)
Common mistakes
- Thinking 5% is a fifth. A fifth is 20%. 5% is one twentieth.
- Taking a percentage of the wrong amount after a change. A 10% rise followed by a 10% fall does not get you back to where you started.
- Moving the decimal point the wrong way: 8% is 0.08, not 0.8.
Quick quiz
Percentages
Check what you know with 5 quick questions.
Question 1 of 5
What is 50% of 60?
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For grown-ups
Related topics
Fractions
A fraction is part of a whole that has been split into equal parts. In ¾, the bottom number says how many equal parts and the top says how many you have.
Decimals
Decimals are numbers with a decimal point. Digits after the point show tenths, hundredths and so on, so 2.5 means two and five tenths.
Ratio
A ratio compares two or more amounts, written with a colon. A ratio of 2:3 means for every 2 of one thing there are 3 of the other.
Equivalent fractions
Equivalent fractions look different but are the same size, like 1/2, 2/4 and 4/8. You make them by multiplying or dividing the top and bottom by the same number.
Compound interest and simple interest
Simple interest is paid only on the starting amount: I = P × r × t. Compound interest is also paid on earlier interest: A = P(1 + r)ⁿ. $1,000 at 10% for 2 years: $1,200 simple, $1,210 compound.
Direct proportion
Two quantities are in direct proportion when one is always the same multiple of the other, so doubling one doubles the other. The rule is y = kx, where k is the constant of proportionality.