Percentages
Percent means for each hundred. A grid of a hundred squares turns a percentage into something you can see: 43% is 43 squares filled, which is also 43/100 and 0.43.
The percentages tool
A hundred squares
Tap a square to fill up to it
0 0/100 0
Percent means "per hundred".
How percentages works
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Fill the hundred squares
Click a square and the grid fills up to it: 43 filled squares out of 100 is 43%, which is 43/100 and 0.43. All three are the same amount, written for three different purposes.
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Use the easy fractions
50% is a half, 25% is a quarter and 10% is a tenth, so 50% of 30 is 15 and 10% of 80 is 8. Anything made of tens and twenty-fives can be built from those three without a calculator.
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Compare on the same footing
Percentages make fair comparisons because both amounts are described out of a hundred: 20% of 100 is 20, while 50% of 10 is only 5. The percentage says how much of the whole, never how big the whole is.
Worked examples
43 squares filled
43%. Forty-three out of a hundred, which is 43/100 and 0.43. The grid is not an illustration of the percentage — it is the percentage.
50% of 30
15. Fifty percent is half, and half of 30 is 15. Halving is the quickest percentage anyone ever finds.
10% of 80
8. Ten percent is a tenth, so divide by ten. From there, 30% is three of those tenths: 8 × 3 = 24.
Where it goes wrong
- Treating 43% as 43 things A percentage is a share of a whole, not a count. 43% of a class of 20 learners is not 43 learners — it is 43 hundredths of 20, which is 8 or 9 of them.
- Assuming a bigger percentage means a bigger amount Fifty percent of 10 is 5, and twenty percent of 100 is 20. The whole decides the size of the amount, so read the percentage and the whole together.
- Dividing by a hundred to find 10% 10% is a tenth, so 10% of 80 is 8, not 0.8. Dividing by a hundred gives 1%; the number of zeros in the denominator tells you how many places to move.
Questions
What does percent actually mean?
It is Latin for "for each hundred", so 43% means 43 for every 100. That is why percentages are so good for comparing: whatever the size of the two things being compared, both are being described out of the same hundred.
How do I find 10% of a number quickly?
Divide by ten. Ten percent of 80 is 8, ten percent of 250 is 25. Once you can do that, you can build the rest: 30% is three tens, 5% is half a ten, and 15% is a ten plus a half of one.
Is 50% always a half?
Always — 50% means 50 out of every 100, which is half of the whole, whatever the whole happens to be. It is half of 10 and half of a million; only the size of the halves differs.
How do percentages relate to fractions and decimals?
They are three spellings of one idea. 43% is 43/100, which is 0.43, which is 43 hundredths — the fraction from rung 8 and the decimal from rung 9, now written out of a hundred so it can be compared with anything else.
Why do shops and reports use percentages all the time?
Because a percentage is scale-free. "Twenty percent off" and "twenty people in a hundred" are the same statement, whether the shop has 100 items or 10,000, and that is what makes a percentage portable from one situation to the next.