# Multiplying Decimals

*Multiply without the decimal point, then re-insert it in the correct spot!*

## 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.

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 *its* 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,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. |

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 |

Here are some more examples:

### 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.