## Content description

Multiply and divide decimals by powers of 10 (ACMNA130)

Source: Australian Curriculum, Assessment and Reporting Authority (ACARA)

### Multiply and divide decimals by powers of 10

When a number is **multiplied** by a power of 10, each digit is **multiplied** by the same power of 10:

When a number is **divided** by a power of 10, each digit is **divided** by the same power of 10:

#### Multiplying whole numbers by 10, 100 and 1000

When 14 is multiplied by 10, the 1 in the tens place is multiplied by 10, and the 4 in the ones place is multiplied by 10.

10 × 10 = 100, and 4 × 10 = 40, and we place a zero in the ones place to say that there are 'no ones'.

14 × 10 = 140

If we multiply 14 by 100:

14 × 100 = 1400

We can extend the pattern:

14 × 10 = 140

14 × 100 = 1400

14 × 1000 = 14 000

14 × 10 000 = 140 000

and so on.