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9.02 Convert units of length


Are you ready?

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


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.

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Example 2

Convert 25.83 millimetres to centimetres. Write your answer as a decimal.

Worked Solution
Create a strategy

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

Apply the idea
\displaystyle 25.83 \text{ mm}\displaystyle =\displaystyle 25.83 \div 10 \text{ cm}Divide by 10
\displaystyle =\displaystyle 2.583 \text{ cm}Decrease the place value of each digit
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.

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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.

\displaystyle 6.22 \text{ km}\displaystyle =\displaystyle 6.22 \times 1000 \text{ m}Multiply by 1000
\displaystyle =\displaystyle 6220 \text{ m}

Then convert this to centimetres by multiplying by 100.

\displaystyle 6220 \text{ m}\displaystyle =\displaystyle 6220 \times 100 \text{ cm}Multiply by 100
\displaystyle =\displaystyle 622\,000 \text{ cm}Add two 0s

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

Idea summary

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

A chart of conversion from kilometres to millimetres. Ask your teacher for more information.



Connect decimal representations to the metric system


Convert between common metric units of length, mass and capacity


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

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