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Units

FoundationChallengeAQAEdexcelOCR

Get to grips with units using these Foundation GCSE Maths practice questions. The worksheet focuses on converting between units of measure, and the accompanying mark scheme breaks down each solution clearly. Suitable for AQA, Edexcel and OCR. Download the questions and answers for free. Multiply when converting to a smaller unit, divide when going to a larger one.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Challenge / Extension

Stretch yourself beyond the basics.

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Topic overview

Metric units follow a consistent decimal structure, which makes converting between them a matter of multiplying or dividing by powers of ten.

For length, \(10\)mm make a centimetre, \(100\)cm make a metre, and \(1000\)m make a kilometre. For mass, \(1000\)g make a kilogram and \(1000\)kg make a tonne. For capacity, \(1000\)ml make a litre.

The direction is what to check. Converting to a smaller unit multiplies and gives a larger number; converting to a larger unit divides and gives a smaller one. A quick sense-check on the size of the answer catches most errors.

Revision notes

The common conversions

Length: \(10\)mm \(= 1\)cm, \(100\)cm \(= 1\)m, \(1000\)m \(= 1\)km.

Mass: \(1000\)g \(= 1\)kg, \(1000\)kg \(= 1\) tonne. Capacity: \(1000\)ml \(= 1\) litre, and \(100\)cl \(= 1\) litre.

Choosing multiply or divide

Converting to a smaller unit multiplies; converting to a larger unit divides.

So \(3\)m is \(300\)cm, but \(450\)cm is \(4.5\)m. The number gets bigger when the unit gets smaller.

Imperial approximations

A few rough equivalents are useful: \(1\)kg is about \(2.2\) pounds, \(1\) litre is about \(1.75\) pints, and \(8\)km is about \(5\) miles.

These are approximate, so answers using them should be given as estimates.

Key points

  • \(10\)mm \(= 1\)cm and \(100\)cm \(= 1\)m.
  • \(1000\)m \(= 1\)km.
  • \(1000\)g \(= 1\)kg.
  • \(1000\)ml \(= 1\) litre.
  • Multiply when converting to a smaller unit.
  • Divide when converting to a larger unit.

Worked examples

Example 1

Convert \(4.5\)km to metres.

Working

\[1\text{km} = 1000\text{m}\]identify the conversion
\[4.5 \times 1000\]multiply, since metres are smaller
\[= 4500\text{m}\]state the answer

Example 2

Convert \(2750\)g to kilograms.

Working

\[1000\text{g} = 1\text{kg}\]identify the conversion
\[2750 \div 1000\]divide, since kilograms are larger
\[= 2.75\text{kg}\]state the answer

Example 3

Convert \(35\)mm to centimetres.

Working

\[10\text{mm} = 1\text{cm}\]identify the conversion
\[35 \div 10\]divide, since centimetres are larger
\[= 3.5\text{cm}\]state the answer

Common mistakes

  • Multiplying when you should divide.

    Converting to a larger unit always gives a smaller number.

  • Using the wrong conversion factor.

    Metres to centimetres is ×100, not ×10.

  • Forgetting the units in the answer.

    A number without a unit is incomplete.

  • Treating imperial approximations as exact.

    They are rough, so answers using them are estimates.

Exam tips

  • Write the conversion factor down before calculating.
  • Sense-check whether the answer should be bigger or smaller.
  • Always include units in your answer.
  • Convert everything to one unit before doing other calculations.

Key terms

Metric
The decimal system of units based on powers of ten.
Tonne
A mass of 1000 kilograms.
Capacity
The amount a container holds.
Approximate
Close to but not exactly equal.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.