# Fractions, Decimals and Percentages

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

We can convert between fractions, decimals and percentages.

## Converting between 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:

## Converting between Percentages and Fractions

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 11100

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 36100

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% = 925

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

36100 = 1850 = 925

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

Example 7: Convert 720 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

720 = 35100 = 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:

## Converting between Fractions and Decimals

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

Example 8: Convert 38 to a decimal.

We can convert 38 to a decimal by calculating 3 ÷ 8.

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

3 ÷ 8 = 0.375

38 = 0.375

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

Example 9 : Convert 712 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...

712 = $$0.58\dot3$$

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% = 88100

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

88100 = 2225

0.88 = 2225

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 1115

Try these: