## Content description

Multiply and divide fractions and decimals using efficient written strategies and digital technologies (ACMNA154)

### Elaborations

- investigating multiplication of fractions and decimals, using strategies including patterning and multiplication as repeated addition, with both concrete materials and digital technologies, and identifying the processes for division as the inverse of multiplication

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

## Multiplication of decimals

### Multiplying by powers of 10

When any number is multiplied by a power of 10, each digit is multiplied by the same power of 10. For example

24.06 × 10 = 20 × 10 + 4 × 10 + 0.06 × 10 = 200 + 40 + 0.6 = 240.6

Multiplying by 10 corresponds to moving the decimal point one place to the right and inserting a zero where necessary.

Similarly, multiplying by 100 (= 10^{2}) corresponds to moving the decimal point two places to the right and inserting zeros where necessary. For example

8.7 × 100 = 870

Multiplying by 1000 (= 10^{3}) corresponds to moving the decimal point three places to the right and inserting zeros where necessary. For example

8.7 × 1000 = 8700

### Dividing by powers of 10

When any number is divided by a power of 10, each digit is divided by the same power of 10. For example:

\begin{align}78.4 ÷ 10&=70÷10+8÷10+0.4÷10\\\\ &=70×\dfrac{1}{10}+8×\dfrac{1}{10}+0.4×\dfrac{1}{10}\\\\ &=7.0+0.8+0.04\\\\ &=7.84\end{align}Dividing by 10 corresponds to moving the decimal point one place to the left and inserting a zero where necessary.

Dividing by 100 (= 10^{2}) corresponds to moving the decimal point two places to the left and inserting zeros where necessary. For example

78.4 ÷ 100 = 0.784

Dividing by 1000 (= 10^{3}) corresponds to moving the decimal point three places to the left and inserting zeros where necessary. For example

78.4 ÷ 1000 = 0.0784