Multiplying Decimals
How to Multiply Decimals
Just follow these steps:
- Multiply without decimal points
- Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
In other words, just count up how many numbers are after the decimal point in both numbers you are multiplying, then the answer should have that many numbers after it's decimal point.
Example: Multiply 0.03 by 1.1
| start with: |
| 0.03 × 1.1 |
| multiply without decimal points: |
| 3 × 11 = 33 |
| 0.03 has 2 decimal places, |
| 0.033 |
How Does It Work?
Because when you multiply without the decimal point (which makes it easy), you are really shifting the decimal point to the right to get it out of the way:
Original: |
| 1 Move: |
| 2 Moves: |
| 3 Moves: |
0.03 × 1.1 |
| 0.3 × 1.1 |
| 3. × 1.1 |
| 3. × 11. |
Then we do the (now easy) multiplication:
3. × 11. = 33.
But remember, we did 3 Moves of the decimal point, so we need to undo that:
3 Moves: |
| 2 Moves: |
| 1 Move: |
| Correct |
33. |
| 3.3 |
| 0.33 |
| 0.033 |
Example: Multiply 0.25 by 0.2
| start with: |
| 0.25 × 0.2 |
| multiply without decimal points: |
| 25 × 2 = 50 |
| 0.25 has 2 decimal places, |
| 0.050 |
Example: Multiply 102 by 0.22
| start with: |
| 102 × 0.22 |
| multiply without decimal points: |
| 102 × 22 = 2,244 |
| 102 has 0 decimal places, |
| 22.44 |
As a final check you can put your "common sense" hat on and think "is that the right size?", because you don't want to pay ten times too much for anything, nor do you want to get only one-tenth of what you need!
And that's all. Just remember: the answer should have the same number of decimal places as are in both numbers you are multiplying.
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