### Converting between Decimals Fractions and Decimals

Decimals, fractions and percentages are all different ways of saying a similar thing and you can convert between them.

Let’s look at some examples:

25% is the same as the fraction which simplifies to

(one quarter) is the same as the decimal 0.25.

So we just saw that 25% is the same as which is the same as 0.25.

Let’s look at some more:

10% = = 0.1

50% = = 0.5

80% = = 0.8

100% = = 1

### Converting to Decimals

## Converting Percentages to Decimals

To turn a percentage in to a decimal, simply take the percentage and **divide it by 100**:

66% = 0.6

The best way to divide by 100 is simply to move the decimal point 2 places left.

## Converting Fractions to Decimals

**To convert fractions to decimals** you have to **divide** the **top number** in the fraction by the **bottom number**:

as a decimal is:

25 ÷ 100 = 0.25

### Converting to Fractions

## Converting Percentages to Fractions

Remember that percentages are ** out of 100**.

**Converting percentages to fractions** is easy. The percentage is already ** out of 100**. So we just need to write the percentage over 100:

66% =

If we want to simplify this we can by dividing top and bottom by 2:

=

## Converting Decimals to Fractions

Converting a decimal to a fraction is a bit more tricky. You would only be asked to do this if the decimal had one or two decimal places.

Here is a method to follow:

- Multiply the decimal by 100 to turn it in to a percentage.
- Write the percentage as a fraction over 100 and simplify if needed.

Let’s look at writing 0.5 as a fraction:

You **times the decimal by 100** changing it in to a percentage:

0.5 x 100 = 50%

Place the percentage over 100:

Next we simplify the fraction if needed, in this case we can divide top and bottom by 50 and simplify it to:

### Converting to Percentages

## Converting Decimals to Percentages

**Converting decimals to percentages** is easy, you simply **multiply the decimal by 100**.

0.3 = 30%

0.85 = 85%

## Converting Fractions to Percentages

Converting fractions to percentages involves two steps:

- First change the percentage in to a decimal by dividing the top number by the bottom number.
- Then times the decimal by 100.

Let’s look at turning in to a percentage:

First we divide 4 by 10:

4 ÷ 10 = 0.4

Then we times by 100:

0.4 x 100 = **40%**

Example

Question: of the audience in a theatre are wearing spacesuits. What percentage of the audience is this?

To convert a fraction to a percentage we first change it to a decimal by dividing the top number by the bottom one:

1 ÷ 5 = 0.2

To do this in your head easily just multiply both numbers by 10 so that the sum is 10 ÷ 5 = 2 and then divide your answer by 10: 2 ÷ 10 = 0.2

Then we multiply 0.2 by 100:

0.2 x 100 = **20%**