Converting Units of Measurement

Video coming soon3 worked examples

Theory

The Golden Rule: decide first whether the unit you are moving to is smaller or larger. Moving to a smaller unit means more of them, so you multiply; moving to a larger unit means fewer of them, so you divide. Checking this before you calculate stops the most common error of all.

1. Metric Length, Weight and Volume

The metric system works entirely in powers of 10:

\text{km} \xrightarrow{\times 1000} \text{m} \xrightarrow{\times 100} \text{cm} \xrightarrow{\times 10} \text{mm}

\text{tonnes} \xrightarrow{\times 1000} \text{kg} \xrightarrow{\times 1000} \text{g} \qquad \text{litres} \xrightarrow{\times 1000} \text{ml}

Reverse each arrow (divide instead) when moving to the larger unit.

2. Units of Area and Volume

This is the part most often got wrong. Because area is two dimensions, the conversion factor is squared; for volume it is cubed:

1\ \text{m}^2 = 100 \times 100 = 10{,}000\ \text{cm}^2

1\ \text{m}^3 = 100 \times 100 \times 100 = 1{,}000{,}000\ \text{cm}^3

Also worth knowing: $1\ \text{cm}^3 = 1\ \text{ml}$ , so $1000\ \text{cm}^3 = 1$ litre.

3. Non-Metric Conversions

You are never expected to memorise conversions such as miles to kilometres — the rate is always given in the question. Simply multiply or divide by the rate given, then check whether your answer is sensible in size.

⚠️ Common Examiner Traps

Area and volume factors: converting $\text{m}^2$ to $\text{cm}^2$ uses $10{,}000$ , not $100$ . This is the single most common conversion error.
Multiplying when you should divide: always ask whether the new unit is smaller (multiply) or larger (divide) before touching the calculator.
Converting too late: in a formula question, convert before substituting, not after — mixing units mid-calculation loses the process marks.
Money-style rounding: a converted measurement is not money — only round to 2 d.p. if the question asks for it.

Worked examples

Example 1

Metric Conversions

Convert: (a) 3.4 km into metres, (b) 250 g into kilograms, (c) 2.5 litres into millilitres.

(a) Metres are smaller than kilometres, so multiply by 1000:

3.4 \times 1000 = 3400\ \text{m}

(b) Kilograms are larger than grams, so divide by 1000:

250 \div 1000 = 0.25\ \text{kg}

(c) Millilitres are smaller than litres, so multiply by 1000:

2.5 \times 1000 = 2500\ \text{ml}

Example 2

🎯 Exam-style (area units)

A workshop floor measures 6 m by 4 m. Floor covering is sold by the square centimetre. Calculate the area of the floor in cm².

Step 1: Find the area in the units given:

6 \times 4 = 24\ \text{m}^2

Step 2: Convert to cm². Because this is an area, multiply by $10{,}000$ , not by 100:

24 \times 10{,}000 = 240{,}000\ \text{cm}^2

(Converting the sides first gives the same answer: $600 \times 400 = 240{,}000$ cm² ✓)

Example 3

Non-Metric Conversion

A driver has enough fuel to travel 150 miles. The destination is 230 km away. Using $1 \text{ mile} = 1.609 \text{ km}$ , determine whether there is enough fuel.

Step 1: Put both distances in the same unit. Convert the range into kilometres by multiplying by the given rate:

150 \times 1.609 = 241.35\ \text{km}

Step 2: Compare with the distance needed, and state a conclusion:

Answer: Yes — there is enough fuel, because $241.35 \text{ km} > 230 \text{ km}$ .

Ready to practise?

10 Converting Units questions with answers and video solutions