In this section, we will consider the multiplication of a decimal by a whole
number, multiplication of a decimal by a power of ten, multiplication of a
decimal by a multiple of a power of ten and multiplication of a decimal by another
decimal.

Multiplication of a Decimal by a Whole Number

Multiplication is repeated addition.

This can be represented on the number line as follows:

Note the following:

This suggests that:

To multiply a decimal number by a whole number:

ignore the decimal point and multiply the digits

place the decimal point in the answer so that it has the same number of
decimal places as the number being multiplied

Example 11

Calculate 45.27 × 6.

Solution:

Note:

There are two decimal places in the decimal number being multiplied.
So,
we place the decimal point two places from the right-hand end of the answer.

Example 12

Calculate 7.382 × 5.

Solution:

Note:

There are three decimal places in the decimal number being multiplied.
So, we place the decimal point three places from the right-hand end of the
answer.

Any trailing zeros in the decimal places of the answer can be
omitted.

In general:

If there are n decimal places in the decimal number being
multiplied, then place the decimal point n places from the right-hand
end of the answer.

Example 13

Calculate 0.0005 × 8.

Solution:

Note:

There are four decimal places in the decimal number being
multiplied. So, we place the decimal point four places from the right-hand
end of the answer.

Any trailing zeros in the decimal places of the answer can be
omitted.

Example 14

Calculate 47.4 × 45.

Solution:

Note:

There is one decimal place in the decimal number being
multiplied. So, we place the decimal point one place from the right-hand
end of the answer.

Any trailing zeros in the decimal places of the answer can be
omitted.