## 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