Fractions, Decimals and Percentages are three different ways of expressing a part of a whole.

We can convert between fractions, decimals and percentages.

To convert a decimal to a percentage we multiply by 100.

**Example 1: Convert 0.7 to a percentage**

To convert a decimal to a percentage we multiply by 100.

0.7 × 100 = 70

0.7 = 70%

**Example 2: Convert 0.19 to a percentage**

To convert a decimal to a percentage we multiply by 100.

0.19 × 100 = 19

0.19 = 19%

To convert a percentage to a decimal we divide by 100

Dividing by 100 is the opposite of multiplying by 100

**Example 3: Convert 25% to a decimal**

To convert a percentage to a decimal we divide by 100.

25 ÷ 100 = 0.25

25% = 0.25

**Example 4: Convert 9% to a decimal**

To convert a percentage to a decimal we divide by 100.

9 ÷ 100 = 0.09

9% = 0.09

**Try these:**

A percentage is out of 100. We can re-write any percentage as a fraction by writing it over 100.

**Example 5: Convert 11% to a fraction.**

A percentage is the same as a fraction out of 100.

We can write 11% as

**Example 6: Convert 36% to a fraction. Give your answer in it simplest form.**

A percentage is the same as a fraction out of 100.

We can write 36% as

We have written 36% as a fraction, but it is not in its simplest form.

To simplify we need to find a times table that 36 and 100 are both in.

36 and 100 are both in the 2 and the 4 times tables.

4 is the biggest so we will divide the denominator and the numerator by 4.

36 = 4 × 9

100 = 4 × 25

36% =

We could have also halved the top and bottom, and then halved again:

To convert a fraction to a percentage we can change the denominator to 100.

**Example 7: Convert 7⁄ 20 to a percentage.**

To convert the fraction to a percentage we need to make the denominator 100.

We can make the denominator 100 by multiplying by 5.

20 × 5 = 100

We have to multiply the numerator by 5 too keep the fraction equivalent.

7 × 5 = 35

When the denominator is not a factor of 100 it may be easier to convert the fraction to a decimal first, and then from a decimal to a percentage.

**Try these:**

To convert from a fraction to a decimal we can divide the numerator by the denominator.

**Example 8: Convert 3⁄ 8 to a decimal.**

We can convert

We can use a calculator or short division to do the calculation.

3 ÷ 8 = 0.375

If we are using a calculator we can also use the SD button.

**Example 9 : Convert 7⁄ 12 to a decimal.**

We need to calculate 7 ÷ 12

7 ÷ 12 = \(0.58\dot3\)

The dot above the 3 means that the 3 is recurring (it goes on forever), 0.5833333333333333333...

To convert a decimal to a fraction we can convert it to a percentage (by multiplying by 100) and then write it is a fraction out of 100.

**Example 10: Convert 0.88 to a fraction. Give your answer in its simplest form.**

To convert 0.88 to a percentage we multiply by 100.

0.88 × 100 = 88

88% =

We can simplify our answer by dividing top and bottom by 4.

0.88 =

If the decimal involves a recurring numbers we can type it into the calculator instead and the calculator will do the conversion for us.

The recurring button looks like this:

It may be found (depending on your calculator) by pressing SHIFT then the square button:

**Example 11: Convert \(0.7\dot3\) to a fraction. Give your answer in its simplest form.**

We can type \(0.7\dot3\) into a calculator by pressing:

The calculator should give an answer of

**Try these:**