Answer:
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
animation 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 arrow 0.3 × 1.1 arrow 3. × 1.1 arrow 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. arrow 3.3 arrow 0.33 arrow 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 = 2244
102 has 0 decimal places,
and 0.22 has 2 decimal place,
so the answer has 2 decimal places:
22.44
