# Fractions, decimals and percentages

The term ‘Per cent’ always means a number ‘out of 100’ and when written as a fraction is always written over a hundred.

For example,

Points to note:

- The percentage fraction must be cancelled to its lowest term if there is a common factor between its numerator and denominator.
- If the fraction is not a whole number, then the equivalent fraction with a whole numbers should be used, again if there is a common factor between its numerator and denominator then it is cancelled down.

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Writing percentages as decimals

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Writing percentages as decimalsPercentages are written as decimals by dividing by 100.

For example,

**Writing fractions as percentages**

When writing a fraction as a percentage, the equivalent fraction is calculated using a denominator of 100. For example:

For example,

**Writing fractions as percentages**

To express a fraction as a percentage, it is multiplied it by 100%.

For example,

Points to note:

- 3/8 is equal to 3/8 x 100% because multiplying by 100% is the same as multiplying by 1.
- Make sure the % sign is written at each stage of the calculation (100 is not the same as 100%!)
- This method works on any fraction regardless of the denominator.

**Writing decimals as percentages**

It is also possible to convert decimals into percentages by multiplying them by 100%.

For example,

0.06 = 0.06 x 100% = 6%

1.245 = 1.245 x 100% = 124.5%

Point to note:

- This can also be carried out using a calculator

**One number as a percentage of another**

John deposited £30 into a bank account. After one year he received 80p interest.

What percentage interest rate he received?

Write 80p out of £32 as a fraction (same units must be used).

Convert the fraction to a percentage.