Basic Conversions
Converting between metric units trips up countless Year 4 pupils who confidently state that 3 metres equals 30 centimetres instead of 300. This fundamental skill bridges primary measurement work with GCSE Foundation topics, where students must fluently convert decimal measurements across length, mass, and capacity units.
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Why it matters
Metric conversions appear everywhere in British life: a 750ml bottle of squash, a 2.5kg bag of flour, or calculating whether 1400m fits within a 1.5km school run. Year 4 pupils first encounter these conversions when measuring classroom objects, progressing to real scenarios like converting ingredient quantities in food technology lessons. By Year 10 GCSE Foundation, students tackle decimal conversions essential for science practicals and engineering contexts. A builder converting 2.3m into millimetres (2300mm) or a pharmacist measuring 0.75kg as 750g relies on automatic recall of these conversion factors. Sports provide compelling examples: Mo Farah's 10,000m race equals exactly 10km, while a 400m track requires 2.5 laps to complete 1km. These conversions underpin scientific literacy, practical problem-solving, and everyday numeracy that students will use throughout their lives.
How to solve basic conversions
Basic Unit Conversions
- To convert to a smaller unit: multiply (e.g. m → cm: ×100).
- To convert to a larger unit: divide (e.g. g → kg: ÷1000).
- Key: 1 km = 1000 m, 1 m = 100 cm, 1 kg = 1000 g, 1 L = 1000 mL.
- Line up units before converting.
Example: 3.5 km = 3.5 × 1000 = 3500 m.
Worked examples
How many cm in 1 m?
Answer: 100
- Remember the conversion factor → 1 m = 100 cm — A ruler is 100 cm long, which is exactly 1 metre. Think of 100 little centimetre marks on a metre stick.
- Think about why it works → 100 cm fit inside 1 m — The prefix tells you: 'kilo' means 1000, 'centi' means 1/100, 'milli' means 1/1000. So 1 m always equals 100 cm.
- State the answer → 100 — There are 100 cm in 1 m.
How many m are in 4 km?
Answer: 4000
- Remember: 1 km = 1000 m → 1 km = 1000 m — This is our conversion factor. We're going from a bigger unit (km) to a smaller unit (m), so each km contains 1000 m.
- Going from bigger to smaller means MULTIPLY → 4 x 1000 = ? — When you break a big unit into smaller pieces, you get MORE pieces. Think of breaking a chocolate bar into squares -- you end up with more squares than bars. So we multiply.
- Calculate → 4 x 1000 = 4000 m — So 4 km = 4000 m. Each of the 4 km contributes 1000 m.
A jogging track is 1500 m. How long is it in km?
Answer: 1.5
- Remember: 1 km = 1000 m → 1 km = 1000 m — We need to convert from m (smaller unit) to km (bigger unit). Each km contains 1000 m.
- Going from smaller to bigger means DIVIDE → 1500 / 1000 = ? — When you group small units into bigger bundles, you get FEWER bundles. Think of putting 1000 gummy bears into bags of 1000 -- you'd have fewer bags than bears. So we divide.
- Calculate → 1500 / 1000 = 1.5 km — 1500 m = 1.5 km. You can check: 1.5 x 1000 = 1500.
Common mistakes
- Students multiply when they should divide, writing 2000g = 20kg instead of 2kg, confusing the direction of conversion between larger and smaller units.
- Pupils forget conversion factors entirely, claiming 1m = 10cm instead of 100cm, often mixing up the powers of 10 for different metric prefixes.
- Converting decimals causes errors like writing 1.5km = 150m instead of 1500m, where students apply the conversion factor to only the whole number part.
- Students add zeros randomly without understanding, converting 3m to 3000cm instead of 300cm, confusing length and mass conversion factors.
- Learners reverse the operation, dividing 5km by 1000 to get 0.005m instead of multiplying to get 5000m when converting to smaller units.