# Adding and Subtracting Decimals

*Adding decimals is easy when you keep your work neat*

To add decimals, follow these steps:

- Write down the numbers, one under the other, with the
**decimal points lined up** **Put in zeros**so the numbers have the same length (see below for why that is OK)**Then add**, using column addition, remembering to put the decimal point in the answer

### Example: Add 1.452 to 1.3

Line up the decimal points: | 1.452 | ||

+ | 1.3 | ||

"Pad" with zeros: | 1.452 | ||

+ | 1.300 | ||

Add: | 1.452 | ||

+ | 1.300 | ||

2.752 |

### Example: Add 3.25, 0.075 and 5

Line up the decimal points: | 3.25 | ||

0.075 | |||

+ | 5. | ||

"Pad" with zeros: | 3.250 | ||

0.075 | |||

+ | 5.000 | ||

Add: | 3.250 | ||

0.075 | |||

+ | 5.000 | ||

8.325 |

That's all there is to it: line up the decimal points, pad with zeros, then add normally.

## Subtracting

To subtract, follow the same method: line up the decimal points, then subtract.

### Example: What is 7.368 − 1.15 ?

Line up the decimal points: | 7.368 | ||

− | 1.15 | ||

"Pad" with zeros: | 7.368 | ||

− | 1.150 | ||

Subtract: | 7.368 | ||

− | 1.150 | ||

6.218 |

**To check** we can add the answer to the number subtracted:

### Example: Check that 7.368 minus 1.15 equals 6.218

Let us try adding 6.218 to 1.15

Line up the decimal points: | 6.218 | ||

+ | 1.15 | ||

"Pad" with zeros: | 6.218 | ||

+ | 1.150 | ||

Add: | 6.218 | ||

+ | 1.150 | ||

7.368 |

It matches the number we started with, so it checks out.

### Putting In Zeros

Why can we put in extra zeros?

A zero is really saying "there is no value at this decimal place".

- In a number like 10, the zero is saying "no ones"
- In a number like 2.50 the zero is saying "no hundredths"

So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc

But DON'T take 2.5 and make it 20.5, that is plain wrong.