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's 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 |
Why line up the decimal points? Because it keeps the digits in their correct place value columns (ones with ones, tenths with tenths, and so on).
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's 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's 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.
Example: Subtracting with Regrouping (5 − 2.34)
| Line up the decimal points: | 5. | ||
| − | 2.34 | ||
| "Pad" with zeros: | 5.00 | ||
| − | 2.34 | ||
| Subtract (regrouping across zeros): | 5.00 | ||
| − | 2.34 | ||
| 2.66 |
Padding with zeros is especially helpful here so we remember that we need to subtract 4 from 0 by regrouping!
Putting In Zeros
Why can we put in extra zeros?
A zero is really saying "there's 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 and so on
But DON'T take 2.5 and make it 20.5, that's plain wrong.