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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.

10%one part in ten25%a quarter50%half of it100%the whole thing
Every percentage is a share of the same imaginary hundred.

  1. Step 1 of 5

    The word says it exactly.

    The per cent sign A hundred dots, twentyof them marked

    'Cent' means hundred. Per cent means for every hundred. Twenty per cent means twenty out of every hundred, whatever the hundred is made of.

  2. Step 2 of 5

    Hundred is chosen, not natural.

    Different bottoms 3/8 versus 5/12 — hardThe same bottom 37.5% versus 41.7% —easy

    Halves and thirds are awkward to compare. Rewriting every share out of the same hundred makes any two of them line up instantly.

  3. Step 3 of 5

    Ten per cent is the one to learn.

    1 £482 10% is £4.803 So 20% is £9.60and 5% is £2.40

    Ten per cent is just the number with the decimal point moved one place left. Every other percentage can be built from it.

  4. Step 4 of 5

    Percentages of different totals are not comparable.

    50% of 8 Four children50% of 800 Four hundred children

    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.

  5. Step 5 of 5

    And percentages of percentages surprise people.

    1 £1002 −50% → £503 +50% → £75, not£100

    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

Per cent means out of a hundred, which makes shares comparable — but only when they are shares of the same total.

Try it yourself

Work out 15% of £60 by finding 10% and then half of it again. It is quicker than any long method.

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