Unit conversions | Year 11

01 / LEARN

Understand the idea.

Understand the idea

A conversion changes the unit used to describe a quantity, not the quantity itself. Since $1 m = 100 cm$ , a length expressed in centimetres has a numerical value 100 times its value in metres. Write the unit relationship before calculating.

For area, both dimensions change. A square with side $1 m$ has side $100 cm$ , so it contains $100^{2} = 10 000$ square centimetres. Volume has three dimensions, giving $100^{3} = 1 000 000$ cubic centimetres per cubic metre.

Choose and apply a method

Identify whether the quantity is a length, area or volume, then use the corresponding linear, squared or cubed conversion factor. When moving to a smaller unit the numerical value increases; when moving to a larger unit it decreases.

Connect capacity to volume using $1 mL = 1 {cm}^{3}$ and $1 L = 1000 {cm}^{3}$ . Consequently $1 m^{3} = 1000 L$ . Keep these links separate from the length factor so litres are not confused with cubic metres.

\begin{aligned} 1 m^{3} & = 1000 L \\ 1 L & = 1000 {cm}^{3} \end{aligned}

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Convert an area

Express 3.6 m $2$ in cm $2$ .

Worked solution

1
Convert the side-length relationship into an area relationship.
$1 m^{2} = {(100 cm)}^{2} = 10 000 {cm}^{2}$
Each of the two dimensions contributes a factor of 100.
2
Convert the given area.
$3.6 m^{2} = 3.6 \times 10 000 = 36 000 {cm}^{2}$
Multiply by the number of square centimetres in each square metre.

Answer

36,000 cm $2$ .

EXAMPLE 02

Convert capacity

A tank has volume 0.84 m $3$ . Express it in litres and millilitres.

Worked solution

1
Use the cubic-metre to litre relationship.
$1 m^{3} = 1000 L$
Litres measure capacity and can be converted from geometric volume.
2
Find the capacity in litres.
$0.84 m^{3} = 0.84 \times 1000 = 840 L$
Each cubic metre contains 1000 litres.
3
Convert litres to millilitres.
$840 L = 840 \times 1000 = 840 000 mL$
Each litre contains 1000 millilitres.

Answer

840 L; 840,000 mL.

03 / YOUR TURN

Try it yourself.

Check your understanding

How many litres are in 2500 cm $3$ ?

Show answer & reasoning

2.5 L.

Since $1000 {cm}^{3} = 1 L$ , divide the volume by 1000: $2500 \div 1000 = 2.5 L$ . The numerical value decreases because litres are the larger unit.

Keep practising

6 worksheet questions · 12 marks

Open worksheet Worked solutions

Read the questions online

Convert 0.375 km to metres.
2 marks
Convert 4800 mm to metres.
2 marks
Convert 2.45 m $2$ to cm $2$ .
2 marks
Convert 65,000 cm $2$ to m $2$ .
2 marks
Convert 0.072 m $3$ to litres.
2 marks
Convert 450 mL to cm $3$ and litres.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Convert 0.375 km to metres.
2 marks
$0.375 \times 1000 = 375$ .
375 m.
Convert 4800 mm to metres.
2 marks
$4800 \div 1000 = 4.8$ .
4.8 m.
Convert 2.45 m $2$ to cm $2$ .
2 marks
$2.45 \times 100^{2} = 24 500$ .
24,500 cm $2$ .
Convert 65,000 cm $2$ to m $2$ .
2 marks
$65 000 \div 10 000 = 6.5$ .
6.5 m $2$ .
Convert 0.072 m $3$ to litres.
2 marks
$0.072 \times 1000 = 72$ .
72 L.
Convert 450 mL to cm $3$ and litres.
2 marks
1 mL equals 1 cm $3$ .
$450 \div 1000 = 0.45$ L.
450 cm $3$ ; 0.45 L.

Checking saved progress…

Curriculum reference & lesson scope

SACE Board of South Australia

Stage 1 General Mathematics measurement skills and applications; original explanatory lessons and papers.

Official curriculum source ↗

In this lesson

Understand the idea.

Understand the idea

Choose and apply a method

See the method in action.

Convert an area

Convert the side-length relationship into an area relationship.

Convert the given area.

Convert capacity

Use the cubic-metre to litre relationship.

Find the capacity in litres.

Convert litres to millilitres.

Try it yourself.

Check your understanding

Keep practising