9.1 Metric Units & Conversions

Measurement questions appear in every ICAS Mathematics paper, and from Papers B to D (Years 4–6) metric conversions are one of the most reliable sources of marks — and of careless errors. Because personal calculators are banned, every conversion must be done by shifting place value, so the students who know the system cold are the ones who answer quickly and correctly.

How the Metric System Is Built

The metric system has one brilliant idea: everything is tens. Every prefix tells you how many of the base unit you have.

The three base units you need are the metre (length), the gram (mass) and the litre (capacity). Attach a prefix and you get a new unit that is exactly 10, 100 or 1000 times bigger or smaller.

The Conversion Ladder

Length

• 1 km = 1000 m
• 1 m = 100 cm
• 1 cm = 10 mm

Mass

• 1 tonne = 1000 kg
• 1 kg = 1000 g

Capacity

• 1 L = 1000 mL

The golden rule: converting to a smaller unit gives you more of them, so you multiply. Converting to a larger unit gives you fewer, so you divide.

Worked example: convert 3.6 km to metres. Metres are smaller than kilometres, so multiply: 3.6 × 1000 = 3600 m. The decimal point simply moves three places right.

Worked example: convert 4500 mL to litres. Litres are larger, so divide: 4500 ÷ 1000 = 4.5 L.

Mixed-Unit Problems

ICAS loves asking you to compare or combine quantities written in different units. The method is always the same: convert everything to one unit before you touch the numbers.

Question style: Which is longer, 1.2 m or 95 cm? Convert 1.2 m to centimetres: 1.2 × 100 = 120 cm. Now compare 120 cm with 95 cm — 1.2 m is longer by 25 cm. Students who compare 1.2 with 95 directly fall into the trap.

Question style: A rope is 2 m 35 cm long. A piece of 80 cm is cut off. How much remains? Convert: 2 m 35 cm = 235 cm. Then 235 − 80 = 155 cm (which is 1 m 55 cm).

Choosing Appropriate Units and Estimating

Papers B–D regularly ask which unit you would use to measure something, or which estimate is reasonable. Anchor these benchmarks in memory:

• A ruler is 30 cm; a doorway is about 2 m; a fingernail is about 1 cm wide.
• A paperclip has a mass of about 1 g; a bag of sugar is 1 kg; a small car is about 1 t.
• A teaspoon holds about 5 mL; a milk carton is 1 L; a bathtub holds about 150 L.

If an option says a pencil has a mass of 2 kg or a classroom is 8 mm long, estimation lets you reject it instantly.

Preview: Area and Volume Conversions

From Paper D upwards, conversions get squared and cubed — and this is the biggest trap of all. If 1 m = 100 cm, then:

• Area: 1 m² = 100 × 100 = 10 000 cm² (not 100!)
• Volume: 1 m³ = 100 × 100 × 100 = 1 000 000 cm³

The length factor gets squared for area and cubed for volume. A useful capacity link: 1 mL = 1 cm³, so 1 L = 1000 cm³.

The Decimal-Shift Method (No Calculator Needed)

Because every conversion factor is 10, 100 or 1000, you never need long multiplication — just move the decimal point. Multiplying by 1000 shifts the point three places right; dividing by 100 shifts it two places left. When digits run out, fill with zeros: 7 kg = 7.000 kg → 7000 g. Practise both directions until each takes under five seconds:

• 0.45 km = 450 m (point moves three right)
• 32 cm = 0.32 m (point moves two left)
• 60 mL = 0.06 L (point moves three left)

A written safety check: after converting, ask whether the number should be bigger or smaller. Metres outnumber kilometres for the same length, so 0.45 km → 450 m (bigger number) is plausible, while 0.45 km → 0.00045 m is not.

Common ICAS Traps in This Topic

• Comparing without converting: 1.05 km looks smaller than 900 m until you write it as 1050 m.
• Wrong factor between cm and mm: 1 cm = 10 mm, not 100 — a 4.7 cm line is 47 mm.
• Forgetting the zero placeholders: 5 kg = 5000 g, not 500 g.
• Area conversions using the length factor: 3 m² is 30 000 cm², not 300 cm².

ICAS multiple-choice options are usually built from exactly these mistakes, so when your answer matches an option too easily, recheck the conversion factor.