## Decimal Numbers

Any number can be written in **decimal form**.

There are three different types of decimal number

- exact,
- recurring
- other decimals.

An **exact or terminating** decimal is one which does *not* go on forever, so you can write down all its digits. For example: 0.15

A **recurring decimal **is a decimal number which does go on forever, but where some of the digits are repeated over and over again. For example: 7.3333333333

Sometimes recurring decimals are written with a bar over the digits which are repeated, or with dots over the first and last digits that are repeated.

**Other decimals** are those which go on forever and don't have digits which repeat. For example pi = 3.141592653589793238462643...

When adding and subtracting decimals add or subtract as normal, but make sure that you keep the decimal points aligned.

For example 3.25 + 1.3 =

3.25

+ 1.30

______

4.55

And to work out 7 - 1.4 we can write it:

7.00

- 1.40

______

5.60

Video to show how to add decimals.

Below is a video to show how you should subtract decimals.

**Multiplying Decimals**

Multiplying decimals is the same as multiplying two whole numbers. You just need to remember the following:

- If there is one digit after the decimal point in the question, there will be one digit after the decimal point in the answer.
- If there are two digits after the decimal point in the question, there will be two digits after the decimal point in the answer etc.

For example to calculate 7.12 × 2 we work out 712 × 2 and then work out where to put the decimal point.

712

× 2

____

1424

There are two digits after the decimal point in the question (7.12 x 2), so there will be two digits after the decimal point in the answer. Therefore 7.12 × 2 = 14.24

This video shows you how to multiply decimals.

**Dividing Decimals**

When dividing a decimal by a whole number, divide as usual but keep the decimal points aligned as in above.

If you are dividing a decimal by another decimal, you need to use equivalent fractions.

For example, 6.12 ÷ 0.2 means 6.12 / 0.2 which is the same as 61.2 / 2 (we have multiplied the numerator and denominator by 10).

Remember to always multiply the numerator and denominator by the same number. And make sure that the denominator is a whole number.

This video shows you how to divide decimals