scholarlab.KS3 Science
Maths Clinic route
MATHS CLINIC · MODULE 1

Units and prefixes

By the end you can: convert between kilo, centi, milli and micro units and check the answer makes sense.

Starting here

Every measurement is a number and a unit. "12" on its own means nothing; "12 cm" tells you exactly how long something is.

A prefix in front of a unit scales it by a power of ten. kilo (k) means 1000 of the unit, centi (c) means one hundredth, milli (m) means one thousandth and micro (µ) means one millionth.

To change to a smaller unit you need more of them, so you multiply. To change to a larger unit you need fewer, so you divide.

Key ideas

  • 1 km = 1000 m · 1 m = 100 cm · 1 cm = 10 mm · 1 mm = 1000 µm
  • 1 kg = 1000 g · 1 litre = 1000 ml = 1000 cm³ · 1 ml = 1 cm³
  • 1 minute = 60 s · 1 hour = 60 minutes
Five boxes in a row: km, m, cm, mm and µm. Arrows to the right are labelled times 1000, times 100, times 10 and times 1000. Arrows to the left are labelled divide by the same numbers.To a smaller unit: multiplykmkilometremmetrecmcentimetremmmillimetreµmmicrometre× 1000÷ 1000× 100÷ 100× 10÷ 10× 1000÷ 1000To a larger unit: divide
Each step to the right is a smaller unit, so the number gets bigger: multiply. Each step to the left is a larger unit: divide. The same prefixes work for grams and litres.

Worked example

A school cross-country course is 1.5 km long. How long is it in metres?

  1. Find the step. km to m is one step to the right on the ladder: a smaller unit, so multiply by 1000.
  2. Calculate. 1.5 × 1000 = 1500
  3. Sense check. Metres are smaller than kilometres, so there should be more of them. 1500 is bigger than 1.5. ✓

Answer: 1500 m

Activities

0 of 5 done

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Now we’ll build those skills by…

…converting in more than one step, comparing measurements given in different units and spotting mistakes.

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Check

6 questions. One try each: get 5 right to complete the module.

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