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## Topic 15: Converting fractions, decimals and percentages

Every number can be expressed as fraction, as a decimal, and as a percentage.

The reason we have these three different formats for expressing the same value is that depending on context, one or the other is usually easier to understand or to work with.

You need to be able to convert numbers from each of the three formats into both of the other formats.

The diagram below may be useful to help visualise these conversions.

Each stage of conversion involves a very simple rule:

• To convert a fraction into a decimal, divide the numerator (at the top) by the denominator (at the bottom).

• To convert a decimal into a percentage, multiply it by 100.

• To convert a percentage into a fraction, place it over 100.

You will be expected to have learnt some conversion facts and equivalencies, so that you don't have to calculate them.

Knowledge of the following facts may be tested in the non-calculator paper.

0.01   = 1%       = 1/100

0.1     = 10%     = 10/100   = 1/10

0.2     = 20%     = 20/100   = 2/10   = 1/5

0.25   = 25%     = 25/100   = 1/4

0.3     = 30%     = 30/100   = 3/10

0.4     = 40%     = 40/100   = 4/10   = 2/5

0.5     = 50%     = 50/100   = 5/10   = 1/2

0.6     = 60%     = 60/100   = 6/10   = 3/5

0.7     = 70%     = 70/100   = 7/10

0.75   = 75%     = 75/100   = 3/4

0.8     = 80%     = 80/100   = 8/10   = 4/5

0.9     = 90%     = 90/100   = 9/10

1        = 100%   = 100/100

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