# 9.02 Convert units of length

Lesson

## Ideas

Can you  multiply decimal numbers  by 10, 100 or 1000?

### Examples

#### Example 1

Find the value of 29.34 \times 100.

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

Here is 29.34 in a place value table:

When we multiply by 100, all the digits move to the left two place values.

29.34\times100 = 2934

Idea summary

We can use a place value table to multiply and divide decimals by powers of 10.

## Convert lengths

If we are comparing two lengths, but they are written in different units we will need to change one of them to perform any calculations.

### Examples

#### Example 2

Worked Solution
Create a strategy

There are 10 millimetres are in 1 centimetre, so we need to divide by 10.

Apply the idea
Idea summary

Remember the following length conversions:

• 1\text{ cm}=10\text{ mm}

• 1\text{ m}=100\text{ cm}

• 1\text{ km}=1000\text{ m}

## Convert between units of length

Convert between units of length in two steps.

### Examples

#### Example 3

Convert 6.22\text{ km} to centimetres.

Worked Solution
Create a strategy

Remember that there are 1000 metres in a kilometre and there are 100 centimetres in a metre.

Apply the idea

Convert 6.22 km to metres first by multiplying by 1000.

Then convert this to centimetres by multiplying by 100.

6.22 \text{ km} = 622\,000 \text { cm}

Idea summary

We can use the following conversion chart to convert between units of measurement.

### Outcomes

#### VCMMG222

Connect decimal representations to the metric system

#### VCMMG223

Convert between common metric units of length, mass and capacity

#### VCMMG224

Solve problems involving the comparison of lengths and areas using appropriate units.