Decimals and Percentages · Grade 6

What is a percentage and how do you convert between percentages, fractions and decimals?

Per cent means out of a hundred, so one per cent is one hundredth. Twenty-five per cent, twenty-five hundredths and a quarter are three ways of writing the same amount. To go from a percentage to a decimal divide by a hundred, and to go the other way multiply by it.

Learning objectives

Out of a hundred

The words per cent mean out of a hundred. Thirty per cent means thirty out of every hundred, so it is exactly thirty hundredths — which as a decimal is nought point three.

It follows that all three forms describe the same amount. Percentage, fraction and decimal are not three topics but three spellings, and the whole skill is moving between them.

A percentage always refers to some whole amount. Fifty per cent of two hundred is not fifty per cent of eighty, so the question of what it is a percentage OF matters just as much as the number itself.

Moving between the forms

From percentage to decimal, divide by a hundred — two places down. Seventy per cent becomes 0.7 and seven per cent becomes 0.07.

From decimal to percentage, multiply by a hundred: two places up. From a fraction, go via a denominator of a hundred — a quarter is twenty-five over a hundred, which is twenty-five per cent.

Worth knowing by heart

A hundred per cent of an amount is all of it, fifty per cent is half, and ten per cent is a tenth — which is a shift of one place down.

From those three you can build a great deal without a calculator. Five per cent is half of ten per cent, twenty per cent is ten per cent doubled, and that covers most everyday sums in your head.

One more shortcut: a percentage of a number equals the number as a percentage of it. Eight per cent of fifty is exactly fifty per cent of eight, which is four — and the second version is almost always the easier one to do mentally.

Worked examples

  1. Write 40 per cent as a decimal and as a fraction in lowest terms

    1. Divide by a hundred: 40 over 100 is 0.4
    2. As a fraction: 40 over 100
    3. Cancel by 20 to get 2 over 5

    Answer: 0.4, which is two fifths

  2. Write three quarters as a percentage

    1. Rewrite with a denominator of a hundred: 3 over 4 is 75 over 100
    2. One hundredth is one per cent

    Answer: 75 per cent

  3. What is 10 per cent of 250, without a calculator?

    1. Ten per cent is a tenth
    2. A tenth means shifting one place down
    3. 250 becomes 25

    Answer: 25

Common mistakes

Writing 5 per cent as 0.5
Five per cent is five hundredths, which is 0.05. The form 0.5 is fifty per cent, ten times more, so this error multiplies the answer by ten.
Calculating a percentage without asking what it is a percentage of
A percentage is always part of some particular amount. Without knowing which, the number means nothing, and in word problems this is exactly what to identify first.
Adding percentages of different wholes
Twenty per cent of a hundred and twenty per cent of two hundred are neither forty per cent nor the same amount. You can add the amounts themselves, never the percentages.

What to remember

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