Multiplying Decimals

In this chapter we shall be looking at multiplying decimal numbers together. This should be straight forward and simple.

Work out 0.6 x 0.8

To work out this easily we’re going to make the decimal numbers whole numbers first.
To turn 0.6 into a whole number we multiply by 10 to get 6;

To turn 0.8 into a while number we multiply by 10 as well to get 80;

Now we can multiply the two simplified whole numbers.

This is not the final answer we have been looking for. We have multiplied the two numbers in the original question by 10. We have to undo these two operations. The opposite of multiplication is division. The answer we got was 48, so we’re going to divide 48 by 10 twice.

We have multiplied by 10 twice and then had to undo the twice operation at the end by dividing the answer by 10 twice.
The following examples explore the same ideas we’ve seen above.

Example 1

Work out 0.4 x 0.12
To simplify this we will have to make the decimals into whole numbers first for an easier calculation. We can turn 0.4 into a whole number by multiplying by 10 as shown below.

…0.4 multiplied by 10 gives us 4.
Now we have to make 0.12 into a whole number as well. We do this by multiplying by 100 as shown below.

…0.12 multiplied by 100 gives 12. Next we have to work out the multiplication of both.

This is not the answer we have been looking for. Throughout we have had to multiply by 10 and 100. We have to reverse these operations on the answer that we have found.

The final answer becomes;

Example 2

Work 0.68 x 0.11
First it would make the all calculation easier if we made the decimal numbers into whole numbers first.
To make 0.68 into a whole number we multiply by 100 as shown below.

..0.68 multiplied by 100 gives us 68. Now we have to turn 0.11 into a whole number as well by multiplying by 100.

…0.11 multiplied by 100 gives use 11. Now lets work out the multiplication of the whole numbers.

This is not the final answer we have been looking for. We have to reverse the multiplying by 100 twice operation.

Example 3

Work out 8.4 x 0.23
Here we have two numbers with different decimal places that we have to multiply together. We have to simplify these two numbers by making each decimal number a whole number.
To 8.4 into a whole number we multiply by 10.

…8.4 multiplied by 10 gives us 84.
We have to also convert 0.23 into a whole number first by multiplying by 100.

…0.23 multiplied by 100 gives us 23. Now let us multiply the whole numbers we have found.

The above is not the final answer. We have to reverse/undo the operations we’re done throughout. First we multiplied by 10 and then multiplied by 100. So we have to reverse this.

The final answer becomes 1.9232. First we multiplied the decimals by 10 and 100 then finally we divided the whole number for the whole numbers multiplication by 100 and 10 to reverse it.