POP

G1.4 Metric Unit Conversions

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01 — Explanation

Which direction do I multiply or divide when converting units?

The metric system is based on powers of 10, so every conversion is just multiplying or dividing by 10, 100, or 1000.

Going from a larger unit to a smaller unit (e.g. km → m): multiply, because you need more of the smaller unit to represent the same amount.
Going from a smaller unit to a larger unit (e.g. cm → m): divide, because fewer of the larger unit are needed.

Exam Tip

Picture a ladder: going down the ladder (to smaller units) means multiplying; going up the ladder (to larger units) means dividing. If you're ever unsure which way to go, sanity-check with a simple case you know — 1 m is clearly more than 1 cm, so cm → m must shrink the number, meaning you divide.

02 — Explanation

What are the key conversion factors for length, mass, and volume?

Quantity	Conversion
Length	$1 \text{ km} = 1000 \text{ m}$ , $\quad 1 \text{ m} = 100 \text{ cm}$ , $\quad 1 \text{ cm} = 10 \text{ mm}$
Mass	$1 \text{ kg} = 1000 \text{ g}$ , $\quad 1 \text{ g} = 1000 \text{ mg}$
Volume	$1 \text{ L} = 1000 \text{ ml}$

Convert 2.5 km to metres: $2.5 \times 1000 = 2500$ m.
Convert 450 cm to metres: $450 \div 100 = 4.5$ m.
Convert 800 g to kilograms: $800 \div 1000 = 0.8$ kg.

03 — Explanation

How do I handle a conversion that crosses two steps, like mm to km?

Break it into one step at a time rather than trying to find a single combined factor. To go from mm to km: first mm → m (divide by 1000), then m → km (divide by 1000 again) — an overall division by $1000 \times 1000 = 1{,}000{,}000$ .

Example: Convert 4,500,000 mm to km.

mm → m: $4{,}500{,}000 \div 1000 = 4500$ m.
m → km: $4500 \div 1000 = 4.5$ km.

Common Mistake

Multiplying instead of dividing when going from a small unit to a large one (or vice versa) because the question "feels" like it should involve a big number. Always decide the direction (bigger or smaller unit) before you decide whether to multiply or divide.

04 — Explanation

How do units of area and volume behave differently from units of length?

Area and volume conversions aren't the same factor as length, because you're squaring or cubing the length conversion. Since $1 \text{ m} = 100 \text{ cm}$ , it follows that $1 \text{ m}^2 = 100^2 = 10{,}000 \text{ cm}^2$ , and $1 \text{ m}^3 = 100^3 = 1{,}000{,}000 \text{ cm}^3$ .

Exam Tip

This is one of the most commonly tested traps at Grade 4+ — students convert $3 \text{ m}^2$ to cm² by multiplying by 100 instead of $100^2$ . Always square (or cube) the linear conversion factor for area (or volume) units.

05 — Worked example

Worked Exam-Style Question

A recipe needs 0.75 litres of milk. A jug can measure in millilitres, marked in steps of 50 ml. How many millilitres of milk are needed, and how many steps of 50 ml is that?

Convert litres to millilitres (larger to smaller unit, so multiply): $0.75 \times 1000 = 750$ ml.
Divide by the step size to find the number of 50 ml steps: $750 \div 50 = 15$ steps.

Exam Tip

When a question combines a unit conversion with a second calculation (like counting "steps" here), always do the conversion first and clearly label your intermediate answer (e.g. " $= 750$ ml") — this secures the method mark even if your final step goes wrong.