Measurement underpins almost every practical task — from buying fabric to mixing concrete to cooking a meal. Foundation Mathematics requires fluency with the metric system: knowing the units, converting between them, and choosing the right unit for each context.
KEY TAKEAWAY: The metric system is built on powers of 10. Once you know the base units and prefixes, conversions are just multiplying or dividing by 10, 100 or 1000.
| Prefix | Symbol | Meaning | Factor |
|---|---|---|---|
| kilo- | k | thousand | $\times 1000$ |
| (base) | — | one | $\times 1$ |
| centi- | c | hundredth | $\div 100$ |
| milli- | m | thousandth | $\div 1000$ |
Base unit: metre (m)
$$1\text{ km} = 1000\text{ m}, \quad 1\text{ m} = 100\text{ cm}, \quad 1\text{ cm} = 10\text{ mm}$$
| Unit | Abbreviation | Typical Use |
|---|---|---|
| kilometre | km | Road distances |
| metre | m | Room dimensions, fabric |
| centimetre | cm | Height, clothing sizes |
| millimetre | mm | Fine measurements, engineering |
Converting:
$$4.5\text{ km} = 4.5 \times 1000 = 4500\text{ m}$$
$$350\text{ mm} = 350 \div 10 = 35\text{ cm} = 350 \div 1000 = 0.35\text{ m}$$
EXAM TIP: Draw a conversion ladder: km → m (×1000), m → cm (×100), cm → mm (×10). Going up the ladder means dividing.
Base unit: square metre ($\text{m}^2$)
Area units are the square of length units, so conversion factors are squared:
$$1\text{ m}^2 = 100^2\text{ cm}^2 = 10000\text{ cm}^2$$
$$1\text{ km}^2 = 1000^2\text{ m}^2 = 1000000\text{ m}^2$$
$$1\text{ ha (hectare)} = 10000\text{ m}^2$$
| Unit | Typical Use |
|---|---|
| $\text{mm}^2$ | Small engineered parts |
| $\text{cm}^2$ | Paper, fabric |
| $\text{m}^2$ | Flooring, walls, land |
| $\text{ha}$ | Farming, large land areas |
| $\text{km}^2$ | Cities, national parks |
Example:
$$1.5\text{ m}^2 = 1.5 \times 10000 = 15000\text{ cm}^2$$
COMMON MISTAKE: Multiplying by 100 when converting $\text{m}^2$ to $\text{cm}^2$. Because both dimensions are scaled, the factor is $100^2 = 10000$, not 100.
Base unit: cubic metre ($\text{m}^3$)
Volume units are the cube of length units:
$$1\text{ m}^3 = 100^3\text{ cm}^3 = 1000000\text{ cm}^3$$
$$1\text{ cm}^3 = 10^3\text{ mm}^3 = 1000\text{ mm}^3$$
| Unit | Typical Use |
|---|---|
| $\text{mm}^3$ | Very small objects |
| $\text{cm}^3$ | Small containers, medicine |
| $\text{m}^3$ | Concrete, soil, large storage |
Capacity measures the internal volume of containers — how much liquid they hold.
$$1\text{ L} = 1000\text{ mL}, \quad 1\text{ kL} = 1000\text{ L}$$
Key link between volume and capacity:
$$1\text{ cm}^3 = 1\text{ mL}, \quad 1000\text{ cm}^3 = 1\text{ L}, \quad 1\text{ m}^3 = 1000\text{ L} = 1\text{ kL}$$
| Unit | Typical Use |
|---|---|
| mL | Medicine, small volumes |
| L | Drinks, fuel, paint |
| kL | Water tanks, swimming pools |
Base unit: kilogram (kg)
$$1\text{ t (tonne)} = 1000\text{ kg}, \quad 1\text{ kg} = 1000\text{ g}, \quad 1\text{ g} = 1000\text{ mg}$$
| Unit | Typical Use |
|---|---|
| mg | Medication dosages |
| g | Food, small items |
| kg | People, groceries, equipment |
| t | Vehicles, bulk materials |
Example:
$$2.4\text{ kg} = 2.4 \times 1000 = 2400\text{ g}$$
$$750\text{ g} = \frac{750}{1000} = 0.75\text{ kg}$$
Always choose a unit that gives a practical number — not too large, not too small.
| Measurement | Poor Choice | Good Choice |
|---|---|---|
| Length of a room | 450 cm | 4.5 m |
| Mass of a letter | 0.025 kg | 25 g |
| Volume of a swimming pool | 2500000 mL | 2500 L or 2.5 kL |
VCAA FOCUS: VCAA tasks often require a unit conversion as part of a larger calculation (e.g. area in $\text{m}^2$ from dimensions given in cm). Always convert to consistent units before calculating.
