Multiplying and Dividing Decimals

Peter Gibby

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.

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.• 1360476 13.60476

5,4,3,2,1

Practice:

• 1.52x0.98=1.5092 (4 decimal places)• 1543.6x20.1=31,026.36 (2 decimal places)• 0.002x1.0006=0.0020012 (7 decimal places)

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.

Example

• If we work that up until the remainder step we get this:

• Now we want to go farther, so what we do is we add a decimal place onto 253, and bring down the 0

5 46 253.0

- 230 230

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 46 253.0

- 230 230- 230 0

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)