Out of a hundred, always
What Does Per Cent Actually Mean?
Per cent just means 'for every hundred', which is why it makes different things comparable.
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Step 1 of 5
The word says it exactly.
The word is the definition. Nobody ever says this part out loud. 'Cent' means hundred. Per cent means for every hundred. Twenty per cent means twenty out of every hundred, whatever the hundred is made of.
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Step 2 of 5
Hundred is chosen, not natural.
Halves and thirds are awkward to compare. Rewriting every share out of the same hundred makes any two of them line up instantly.
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Step 3 of 5
Ten per cent is the one to learn.
Ten per cent is just the number with the decimal point moved one place left. Every other percentage can be built from it.
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Step 4 of 5
Percentages of different totals are not comparable.
Fifty per cent of a class of eight and fifty per cent of a school of eight hundred are the same fraction and wildly different numbers of children.
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Step 5 of 5
And percentages of percentages surprise people.
A price cut by fifty per cent and then raised by fifty per cent does not come back. The second fifty is fifty of a smaller number.
This is why a shop can honestly advertise a big rise as a small percentage and a small fall as a big one.
The short version
A hundred is chosen, not natural — a common denominator so any two shares line up, with ten per cent the decimal point moved one place. But percentages do not stack: down fifty per cent then up fifty leaves you short.
Try it yourself
Work out 15% of £60 by finding 10% and then half of it again. It is quicker than any long method.