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.
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