Length/Distance	\text{mm, cm, m, km}
Area	\text{mm}^{2}, \text{cm}^{2}, \text{m}^{2}, \text{km}^{2}
Volume	\text{mm}^{3}, \text{cm}^{3}, \text{m}^{3}, \text{km}^{3}
Capacity	\text{mL, L, kL, ML}
Weight (mass)	\text{mg, g, kg, metric tonne}
Time	\text{sec, mins, hrs, days, weeks, months, years}

Ideas

Length
Area
Volume
Capacity

Length

When comparing two lengths written in different units it is necessary to change one of them. To convert between different units of measure recall that it will be necessary to multiply or divide by powers of 10.

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.

If we need to convert a length from kilometres (\text{km}) to centimetres (\text{cm}), it could be completed in one big step. Alternatively using smaller steps can support the process and reduce errors.

Examples

Example 1

Convert 6.52\text{ cm} to millimetres.

Worked Solution

Create a strategy

Use the conversion 1 \text{ cm}= 10 \text{ mm}.

Apply the idea

We need to multiply the centimetres by 10.

\displaystyle 6.52 \text{ cm}	\displaystyle =	\displaystyle 6.52 \times 10 \text{ mm}	Multiply by 10
	\displaystyle =	\displaystyle 65.2 \text{ mm}	Evaluate

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

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}

Example 4

Convert 512\,200 cm to kilometres. Write your answer as a decimal.

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 512\,200 cm to metres first by dividing by 1000.

\displaystyle 512\,200 \text{ cm}	\displaystyle =	\displaystyle 512\,200 \div 1000 \text{ m}	Divide by 1000
	\displaystyle =	\displaystyle 512.2 \text{ m}

Then convert this to kilometres by dividing by 100.

\displaystyle 512.2 \text{ m}	\displaystyle =	\displaystyle 512.2 \div 100 \text{ km}	Divide by 100
	\displaystyle =	\displaystyle 5.122 \text{ km}	Evaluate

512\,200 \text{ cm} = 5.122 \text { km}

Example 5

Convert 2.12\text{ km} to millimetres.

Worked Solution

Create a strategy

Remember that there are 1000 metres in a kilometre, there are 100 centimetres in a metre and there are 10 millimetres in a centimetre.

Apply the idea

Convert 2.12 km to metres first by multiplying by 1000.

\displaystyle 2.12 \text{ km}	\displaystyle =	\displaystyle 2.12 \times 1000 \text{ m}	Multiply by 1000
	\displaystyle =	\displaystyle 2120 \text{ m}

Then convert this to centimetres by multiplying by 100.

\displaystyle 2120 \text{ m}	\displaystyle =	\displaystyle 2120 \times 100 \text{ cm}	Multiply by 100
	\displaystyle =	\displaystyle 212\,000 \text{ cm}	Evaluate

Then convert this to millimetres by multiplying by 10.

\displaystyle 212\,000 \text{ cm}	\displaystyle =	\displaystyle 212\,000 \times 10 \text{ mm}	Multiply by 10
	\displaystyle =	\displaystyle 2\,120\,000 \text{ mm}	Evaluate

2.12 \text{ km} = 2\,120\,000 \text { mm}

Example 6

A skyscraper is 961 metres tall.

What is the height of the building in kilometres? Give your answer in decimal form.

Worked Solution

Create a strategy

Use the conversion 1 \text{ km}= 1000 \text{ m}.

Apply the idea

We need to divide the metres by 1000.

\displaystyle 961 \text{ m}	\displaystyle =	\displaystyle 961 \div 1000 \text{ m}	Multiply by 1000
	\displaystyle =	\displaystyle 0.961 \text{ km}	Evaluate

What is the height of the building in centimetres?

Worked Solution

Create a strategy

Use the conversion 1 \text{ m}= 100 \text{ cm}.

Apply the idea

We need to multiply the metres by 100.

\displaystyle 961 \text{ m}	\displaystyle =	\displaystyle 961 \times 100 \text{ cm}	Multiply by 100
	\displaystyle =	\displaystyle 96\,100 \text{ cm}	Evaluate

Idea summary

Use the following conversion chart to convert between units of measurement.

Area

Converting units of area:

Area is described as units squared so when converting units of measure for area, use the same system as for length except square the power of 10. That is, if converting from\text{m}^2 to \text{cm}^2 look for the conversion number from \text{m} to \text{cm}, and square it. In other words, converting an area in \text{m}^2 to \text{cm}^2 requires us to multiply the area by 100^{2}.

Examples

Example 7

Convert 6\text{ m}^{2} to \text{ cm}^{2}.

Worked Solution

Create a strategy

Use the conversion 1 \text{ m}^2= 10\,000 \text{ cm}^2.

Apply the idea

\displaystyle 6\text{ m}^{2}	\displaystyle =	\displaystyle 6 \times 10\,000	Multiply by 10\,000
	\displaystyle =	\displaystyle 60\,000\text{ cm}^{2}	Evaluate

Example 8

Convert 0.56 \text{ km}^2 into \text{m}^2.

Worked Solution

Create a strategy

Use the conversion 1 \text{ km}^2= 1\,000\,000 \text{ m}^2.

Apply the idea

\displaystyle 0.56 \text{ km}^2	\displaystyle =	\displaystyle 0.56 \times 1\,000\,000	Multiply by 1\,000\,000
	\displaystyle =	\displaystyle 560\,000 \text{ m}^2	Evaluate

Example 9

Convert 790\,000\,000\text{ cm}^2 to \text{ km}^2.

Worked Solution

Create a strategy

Remember that there are 1\,000\,000\text{ m}^{2} in a\text{ km}^{2} and there are 10\,000\text{ cm}^{2} in a \text{m}^{2}.

Apply the idea

Convert 790\,000\,000\text{ cm}^2 to \text{ m}^{2} first by dividing by 10\,000.

\displaystyle 790\,000\,000\text{ cm}^2	\displaystyle =	\displaystyle \dfrac{790\,000\,000}{10\,000\text{ m}^{2}}	Divide by 10\,000
	\displaystyle =	\displaystyle 79\,000 \text{ m}^{2}

Then convert this to \text{ km}^{2} by dividing by 1\,000\,000.

\displaystyle 79\,000 \text{ m}^{2}	\displaystyle =	\displaystyle \dfrac{79\,000}{1\,000\,000\text{ km}^{2}}	Divide by 1\,000\,000
	\displaystyle =	\displaystyle 0.079 \text{ km}^{2}	Evaluate

Idea summary

Area is described as units squared so when converting units of measure for area, use the same system as for length except square the power of 10.

Volume

Converting units of volume:

Volume is described as units cubed so when converting units of measure for volume, use the same system as for length except cube the power of 10. That is, if converting from \text{m}^3 to \text{cm}^3 look for the conversion number from \text{m} to \text{cm}, and cube it. In other words, converting a volume in \text{m}^3 to \text{cm}^3 requires us to multiply the area by 100^{3}.

Examples

Example 10

Convert 19\,420\text{ cm}^3 to litres.

Worked Solution

Create a strategy

Use the conversion 1\text{ L} = 1000\text{ cm}^3.

Apply the idea

\displaystyle 19\,420\text{ cm}^3	\displaystyle =	\displaystyle 19\,420 \div 1000	DIvide by 1000
	\displaystyle =	\displaystyle 19.42\text{ litres}	Evaluate

\displaystyle 19\,420\text{ cm}^3

\displaystyle =

\displaystyle 19.42\text{ litres}

Idea summary

Volume is described as units cubed so when converting units of measure for volume, use the same system as for length except cube the power of 10.

Capacity

Capacity is the amount of liquid that a container can hold. Capacity is usually measured using one of the following units:

millilitres (\text{mL})
litres (\text{L})
kilolitres (\text{kL})
megalitres (\text{ML})

Most of these will be familiar from previous experiences, such as the size of your milk container, measuring ingredients when cooking, measuring medicines or even in science experiments you may have done at school.

1\text{ L} = 1000 \text{ mL}

1\text{ kL} = 1000 \text{ L} = 1\,000\,000 \text{ mL } (1000 \times 1000)

1\text{ ML} = 1000 \text{ kL} = 1\,000\,000 \text{ L } = 1\,000\,000\,000\text{ mL}

A diagram that shows how to convert between millilitres, litres, kilolitres, and megalitres.

Notice that the prefixes of milli and kilo are used again. Remember that the prefix 'milli' means \dfrac{1}{1000}\text{th} of something. A millilitre is \dfrac{1}{1000}\text{th} of a litre, which means that there are 1000 \text{ mL} in 1 litre. Also the prefix 'kilo' means 1000 lots of something, so a kilolitre is 1000 litres.

Examples

Example 11

Convert 4920 millilitres to litres.

Worked Solution

Create a strategy

Remember that 1 litre = 1000 millilitres.

To convert millilitres to litres, divide by 1000.

Apply the idea

Here is 4920 in a place value table.

Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths
4	9	2	0

To divide by 1000 we move each digit to the right three places.

Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths
			4	.	9	2

4920 \div 1000 = 4.92

4920 millilitres = 4.92 litres.

Idea summary

Converting Capacity:

1\text{ L} = 1000 \text{ mL}

1\text{ kL} = 1000 \text{ L} = 1\,000\,000 \text{ mL } (1000 \times 1000)

1\text{ ML} = 1000 \text{ kL} = 1\,000\,000 \text{ L } = 1\,000\,000\,000\text{ mL}

Outcomes

U2.AoS4.1

the measures of length, area, volume and capacity and their units of measurement

10.02 Measurement units

Introduction

Ideas

Length

Examples

Example 1

Example 2

Example 3

Example 4

Example 5

Example 6

Area

Examples

Example 7

Example 8

Example 9

Volume

Examples

Example 10

Capacity

Examples

Example 11

Outcomes

U2.AoS4.1

What is Mathspace

About Mathspace