How to Multiply Decimals
Just follow these steps:- Multiply normally, ignoring the decimal points.
- Then put the decimal point in the answer - it will have as many decimal places as the two original numbers combined.
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,
and 1.1 has 1 decimal place, so the answer has 3 decimal places: |
0.033 |
 |
See the Multiplying Decimals Animations |
How Does It Work?
Because when you multiply without the decimal point, 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. |
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,
and 0.2 has 1 decimal place, so the answer has 3 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,
and 0.22 has 2 decimal place, so the answer has 2 decimal places: |
22.44 |
Common Sense
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 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 the numbers you are multiplying.
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