Year 7 Interactive Maths - Second Edition

## Multiplication of Decimals

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

This can be represented on the number line as follows:

###### 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.