1. Multiplying and Dividing Decimals
Peter Gibby

2. Multiplying
The trick with decimals is to line them up, do the work as if they were not there, then put it back. The biggest change from adding to multiplying decimals is that we can’t just drop the decimal from the problem. We count the amount of places from both numbers and add them together. That number tells us how many decimal places we will have.

3. Example
12.92x1.053
We can remove the decimals after counting the number of places. There are 5.
Now we use long multiplication:
1,292x1,053= 1,360,476
We count out, from the right 5 places and place the decimal there.
5,4,3,2,1

4. Practice: 1.52x0.98=1.5092 (4 decimal places)

5. Division
Division with decimals is just like long division, once we take care of decimal places. But with them, we can get a much more exact answer!
Lets look at 25.3/4.6
Firstly we can cancel out decimal places, since there are one in each, we can rewrite this as: 253/46 it just becomes long division.

6. Example If we work that up until the remainder step we get this: 5
Now we want to go farther, so what we do is we add a decimal place onto 253, and bring down the 0 5
- 230
230

7. Finishing example
Now we add the decimal place right above
We continue long division
We can continue adding decimal places and dropping the 0 down, but we get to stop here.
5.5
- 230
230
- 230

8. Checking Example
If you didn’t believe that we could just cancel the decimal place at the beginning of the example, we can check it now.
If we multiply 4.6 and 5.5 we should get 25.3
4.6x5.5 (2 decimal places)
46x55=2530
Add the decimals back:
4.6x5.5=25.30=25.3 (a 0 at the end of a decimal means just as much as a 0 before the rest of a whole number, 025=25 and .250=.25)