Units of Measure #
IGCSE Mathematics Topic 5.1 (Mensuration) – Using metric units and converting between different units
Length Units #
Length measures how long something is. The basic metric unit is the metre (m).
$1 \text{ cm} = 10 \text{ mm}$ | $1 \text{ m} = 100 \text{ cm}$ | $1 \text{ km} = 1000 \text{ m}$
Worked Example 1 #
Question: Convert 3.5 km to metres.
Solution: Big unit → small unit, so multiply
$3.5 \times 1000 = 3500 \text{ m}$
Worked Example 2 #
Question: Convert 450 cm to metres.
Solution: Small unit → big unit, so divide
$450 \div 100 = 4.5 \text{ m}$
Mass Units #
Mass measures how much matter is in an object. The main units are grams (g) and kilograms (kg).
$1 \text{ kg} = 1000 \text{ g}$
Worked Example 3 #
Question: A bag of rice weighs 2.5 kg. What is its mass in grams?
Solution: Big unit → small unit, so multiply
$2.5 \times 1000 = 2500 \text{ g}$
Area Units #
Area measures the size of a flat surface. Because area = length × width, we use square units like $\text{cm}^2$ or $\text{m}^2$.
- A square that is 1 m × 1 m is also 100 cm × 100 cm
- Area = $100 \times 100 = 10000 \text{ cm}^2$
IMAGE NEEDED: Diagram showing a 1m × 1m square divided into a 100 × 100 grid of 1cm squares, demonstrating why 1 m² = 10,000 cm²
Google Images Search: “1 square metre equals 10000 square centimetres grid diagram IGCSE maths”
$1 \text{ cm}^2 = 100 \text{ mm}^2$ ($10^2$)
$1 \text{ m}^2 = 10000 \text{ cm}^2$ ($100^2$)
$1 \text{ km}^2 = 1000000 \text{ m}^2$ ($1000^2$)
Worked Example 4 #
Question: Convert $2.5 \text{ m}^2$ to $\text{cm}^2$.
Solution: Big unit → small unit, so multiply by 10000
$2.5 \times 10000 = 25000 \text{ cm}^2$
Worked Example 5 #
Question: Convert $600 \text{ cm}^2$ to $\text{m}^2$.
Solution: Small unit → big unit, so divide by 10000
$600 \div 10000 = 0.06 \text{ m}^2$
Volume Units #
Volume measures the space inside a 3D object. Because volume = length × width × height, we use cubic units like $\text{cm}^3$ or $\text{m}^3$.
- A cube that is 1 m × 1 m × 1 m is also 100 cm × 100 cm × 100 cm
- Volume = $100 \times 100 \times 100 = 1000000 \text{ cm}^3$
$1 \text{ cm}^3 = 1000 \text{ mm}^3$ ($10^3$)
$1 \text{ m}^3 = 1000000 \text{ cm}^3$ ($100^3$)
Worked Example 6 #
Question: A box has a volume of $0.5 \text{ m}^3$. What is this in $\text{cm}^3$?
Solution: Big unit → small unit, so multiply by 1000000
$0.5 \times 1000000 = 500000 \text{ cm}^3$
Capacity Units #
Capacity measures how much liquid a container can hold. The main units are millilitres (ml) and litres (l).
$1 \text{ litre} = 1000 \text{ ml}$
Volume and Capacity Connection #
$1 \text{ ml} = 1 \text{ cm}^3$
$1 \text{ litre} = 1000 \text{ cm}^3$
$1 \text{ m}^3 = 1000 \text{ litres}$
- 1 litre is the volume of a cube measuring 10 cm × 10 cm × 10 cm
- Volume = $10 \times 10 \times 10 = 1000 \text{ cm}^3$
IMAGE NEEDED: 3D diagram showing a 10 cm × 10 cm × 10 cm cube labeled as 1 litre = 1000 cm³
Google Images Search: “1 litre equals 1000 cubic centimetres 10cm cube diagram IGCSE”
Worked Example 7 #
Question: A fish tank has a volume of $24000 \text{ cm}^3$. How many litres can it hold?
Solution: Since $1 \text{ litre} = 1000 \text{ cm}^3$, divide by 1000
$24000 \div 1000 = 24 \text{ litres}$
Worked Example 8 #
Question: A water tank has a volume of $2.5 \text{ m}^3$. What is its capacity in litres?
Solution: Since $1 \text{ m}^3 = 1000 \text{ litres}$, multiply by 1000
$2.5 \times 1000 = 2500 \text{ litres}$
Summary: All Key Conversions #
| Type | Conversion |
|---|---|
| Length | $1 \text{ cm} = 10 \text{ mm}$ | $1 \text{ m} = 100 \text{ cm}$ | $1 \text{ km} = 1000 \text{ m}$ |
| Mass | $1 \text{ kg} = 1000 \text{ g}$ |
| Area | $1 \text{ cm}^2 = 100 \text{ mm}^2$ | $1 \text{ m}^2 = 10000 \text{ cm}^2$ | $1 \text{ km}^2 = 1000000 \text{ m}^2$ |
| Volume | $1 \text{ cm}^3 = 1000 \text{ mm}^3$ | $1 \text{ m}^3 = 1000000 \text{ cm}^3$ |
| Capacity | $1 \text{ litre} = 1000 \text{ ml}$ |
| Volume ↔ Capacity | $1 \text{ ml} = 1 \text{ cm}^3$ | $1 \text{ litre} = 1000 \text{ cm}^3$ | $1 \text{ m}^3 = 1000 \text{ litres}$ |
