Metric units and conversions
Convert between metric units of length, area, mass, volume and capacity; use standard prefixes and scientific notation.
Worked examples
Converting between metric units of length
Straightforward
Problem
Convert km to centimetres.
1
Convert kilometres to metres by multiplying by .
m
2
Convert metres to centimetres by multiplying by .
cm
3
State the answer with units.
km cm
Answer
cm
Converting between units of volume and capacity
Moderate
Problem
A fish tank has a volume of cm³. Express this volume in litres and in kilolitres.
1
Convert cm³ to mL using the fact that cm³ mL.
cm³ mL
2
Convert mL to L by dividing by .
L
3
Convert L to kL by dividing by .
kL
4
State both answers with units.
cm³ L kL
Answer
L or kL
Multi-step conversion — volume in litres
Challenging
Problem
A rectangular garden bed is cm long, cm wide and cm deep. Find the volume of soil needed in litres.
1
Calculate the volume of the garden bed in cm³.
cm³
2
Convert cm³ to mL using cm³ mL.
cm³ mL
3
Convert mL to L by dividing by .
L
4
State the answer with units.
Volume of soil L
Answer
L
Practise
Q1·Straightforward
Convert cm to metres.
Explanation
m
Q2·Straightforward
Convert km to metres.
Explanation
m
Q3·Straightforward
Convert ha to square metres.
Explanation
m²
Q4·Straightforward
Convert g to kilograms.
Explanation
kg
Q5·Moderate
A container holds cm³ of water. Express this volume in millilitres.
Explanation
Since cm³ mL, cm³ mL.
Q6·Moderate
Convert m³ to kilolitres.
Explanation
Since m³ kL, m³ kL.
Q7·Moderate
A strand of hair is nanometres wide. Which of the following correctly expresses this width in metres using scientific notation? ( nm m)
Explanation
m
Q8·Moderate
A storage tank holds m³ of water. Find the volume in litres.
Explanation
L
Q9·Challenging
A rectangular tank is cm long, cm wide and cm deep. Find its capacity in kilolitres.
Explanation
Volume cm³. Converting: cm³ mL L kL.
Q10·Challenging
A rectangular swimming pool is m long, m wide and m deep. Find its capacity in megalitres.
Explanation
Volume m³ kL ML.
Q11·Challenging
A paddock has an area of km². Express this area in hectares.
Explanation
ha
Q12·Challenging
A cylindrical water tank has a radius of m and a height of m. Find its capacity in kilolitres. Use .
Explanation
m³ kL.