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GCSE Maths Ratio and Proportion

Units Of Measurement

Units Of Measurement

Here we will learn about units of measurement from the metric system and imperial system including how to convert between them.

There are also units of measurement worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What are units of measurement?

Units of measurement are used to measure different quantities.

What are units of measurement?

What are units of measurement?

Metric units of measurement

Metric units of measurement are the measurements which are used internationally.

Metric standard units form part of the international system of units (SI units) and use a variety of abbreviations for common units.

For example,

The metric unit of measurement for length is the metre (m) ,

The metric unit of measurement for mass is the gram (g),

The metric unit of measurement for capacity is the litre (l).

Units of measurement HUB Image 1

For smaller quantities or larger quantities we can adapt the metric units of measurement. The main ones used are kilo, centi and milli:

Units of measurement HUB Image 2

Step-by-step guide: Metric units of measurement

Imperial units of measurement

Imperial units of measurement are an older system of measurements but some are still used in everyday life.

For example,

1 \;inch ≈ 2.5 \;cm

1 \;foot ≈ 30 \;cm

1 \;mile ≈ 1.6 \;km

Conversion of units

Conversion of units is when we need to change from one unit to another. This may be between imperial units and metric units.

For example,

5 \;miles ≈ 8 \;kilometres

Step-by-step guide: Conversion of units

Converting metric units

Converting metric units is when we convert between different metric units of measurement by multiplying or dividing by powers of 10.

For example,

7.1 \;cm ≈ 71 \;mm

Units of measurement HUB Image 3

Step-by-step guide: Converting metric units

Converting units of area and volume

Converting units of area and volume allows us to convert between different metric units in questions involving area and volume.

We do this by adapting how we convert  units of length.

Units of measurement HUB Image 4

Step-by-step guide: Converting units of area and volume

Converting units of time

Converting units of time is when we have information about time in one unit, but we need to change the time into a different unit. 

We need to know that:

1 hour = 60 minutes

1 minute = 60 seconds

For example,

Give 3.2 hours as hours and minutes.

0.2\times 60=12 minutes.

3.2 hours is 3 \; hours and 12 minutes

Step-by-step guide: Converting units of time

Converting units of length

Converting units of length is when we have information about a length in one unit, but we need to change the length into a different unit. 

For example we could be given a height of a person in centimetres, but need to convert it to metres.

For example, 174 cm = 1.74 m.

Converting units of mass, time, area

Converting units also extends to units other than length. It can include mass, times or areas. 

For example we could be given a mass in kilograms, but need to convert it to grams.

For example, 1.26 kg = 1260 g.

This is because there are 1000 grams in 1 kilogram.

For example we could be given a time in hours, but need to convert it to minutes.

For example, 3.4 hours = 204 minutes.

This is because 1 hour is 60 minutes, so 3 hours will be 180 minutes. 0.4 of an hour is 24 minutes. So 3.4 hours will be 204 minutes.

For example we could be given an area in square centimetres and asked to convert to square millimetres.

For example, 7.2 cm2 = 720 mm2.

This is because 1 square centimetre is 100 square millimetres.

How to use units of measurement

In order to use units of measurement:

  • Check what is being measured.
  • Check if metric units are being used.
  • Check if a conversion is required.
  • Check the conversion factor.
  • Check if area or volume is involved.

Explain how to use units of measurement

Explain how to use units of measurement

Units of measurement worksheet

Get your free units of measurement worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Units of measurement worksheet

Get your free units of measurement worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Units of measurement examples

Example 1: choosing a metric unit of measurement

Write down a sensible metric unit of measurement for:

The weight of a packed suitcase.

  • Check what is being measured.

The weight of an object is being measured. So we need to consider units of mass.

  • Check if metric units are being used.

The question asks for metric units, so we need to consider grams or kilograms.

Kilograms would be the most sensible metric unit of measurement for a packed suitcase.

Example 2: conversion of units – metric/imperial

Use 1 \; inch \; 2.54 \; cm

Convert:

5 \; inches to cm

Check if a conversion is required.

Check the conversion factor.

Example 3: conversion of units – metric/imperial

Use 5 \; miles \; ≈ \; 8 \; km

Convert:

60 \; miles to km

Check if a conversion is required.

Check the conversion factor.

Example 4: conversion of units – speed

Convert:

8 \; m/s to km/h

Check if a conversion is required.

Check the conversion factor.

Example 5: converting metric units

Convert:

9.6 \; l to ml

Check if metric units are being used.

Check if a conversion is required.

Check the conversion factor.

Example 6: converting metric units

Convert:

780 \; cm to m

Check if metric units are being used.

Check if a conversion is required.

Check the conversion factor.

Example 7: converting units of area and volume

Convert:

2.3 \; cm^2 to mm^2

Check if metric units are being used.

Check if a conversion is required.

Check the conversion factor.

Check if area or volume is involved.

Example 8: converting units of time

Convert:

2.7 hours to minutes

Check what is being measured.

Check the conversion factor.

Common misconceptions

  • Multiply or divide?

Remember:

– if you are going from larger units to smaller units – multiply

– if you are going from smaller units to larger units – divide

  • Prefix

A common error is to mix up the different prefixes i.e. milli, kilo, centi etc.

  • Fractions of an hour

Remember that time is not a decimal system based on 10 . A quarter of an hour is 15 minutes.  But one quarter as a decimal is 0.25 . E.g. 3.25 hours is 3 hours and 15 minutes. Similarly 1\frac{1}{2} days is 1 day and 12 hours.

Practice units of measurement questions

1. Choose the most sensible metric unit to measure:

 

The volume of a coffee cup

grams

GCSE Quiz False

pints

GCSE Quiz False

millilitres

GCSE Quiz True

litres

GCSE Quiz False

We need a unit for capacity – so grams can be ruled out. We need a metric unit – so pints can be ruled out. The volume of a teaspoon is very small, so millilitres are the best unit.

2. Use the conversion 1 \; foot ≈ 0.3 \; m, convert 4.5 \; m to feet:

20 \; feet
GCSE Quiz False

18 \; feet
GCSE Quiz False

15 \; feet
GCSE Quiz True

12 \; feet
GCSE Quiz False

We need to divide by 0.3

 

4.5\div 0.3=15

 

So 4.5 \; m is approximately 15 \; feet

3. Convert: 5.3 \; l to ml

53 \; ml
GCSE Quiz False

53 \ 000 \; ml
GCSE Quiz False

530 \; ml
GCSE Quiz False

5300 \; ml
GCSE Quiz True

Converting litres to millilitres we multiply by 1000.

 

5.3 \times 1000=5300

 

So 5.3 \; l is approximately 5300 \; ml

4. Convert: 18 \; km/h to m/s

6 \; m/s
GCSE Quiz False

5 \; m/s
GCSE Quiz True

8 \; m/s
GCSE Quiz False

7 \; m/s
GCSE Quiz False

Converting kilometres to metres we multiply by 1000.

 

Converting to metres per hour

 

18 \times 1000 =18\ 000

 

Converting to metres per minute

 

18\ 000 \div 60 = 300

 

Converting to metres per minute

 

300 \div 60 = 5

 

So 18 \; km/h is equal to 5 \; m/s

5. Convert: 700 \; mm^2 to cm^2

0.7 \; cm^2
GCSE Quiz False

7000 \; cm^2
GCSE Quiz False

70 \; cm^2
GCSE Quiz False

7 \; cm^2
GCSE Quiz True

Converting square millimetres to square centimetres we divide by 10^2 .

 

700 \div 10^2 = 700 \div 100 = 7

 

So 700 \; mm^2 is equal to 7 \; cm^2

6. Convert: 2 \; m^3 to cm^3

200 \; cm^3
GCSE Quiz False

2\ 000 \ 000 \; cm^3
GCSE Quiz True

20 \ 000 \; cm^3
GCSE Quiz False

200 \ 000 \; cm^3
GCSE Quiz False

Converting cubic metres to cubic centimetres we multiply by 100^3 .

 

2 \times 100^3 = 2 \times 1 \ 000 \ 000 = 2 \ 000 \ 000

 

So 2 \; m^3 is equal to 2 \ 000 \ 000 \; cm^3

Units of measurement GCSE questions

1. Circle the best metric unit of measurement for:

The weight of a horse

 

litres       kilograms       pounds       grams

 

(1 mark)

Show answer

Kilograms

(1)

2. A bottle contains 1.5 litres of cola.

A can contains 330 \; ml of cola.

 

Charlier has 3 bottles of cola and 4 cans of cola.

How much cola do they have in total?

Give your answer in millilitres.

 

(3 marks)

Show answer
1.5 \times 1000=15000

(1)

 

3 \times 1500+4 \times 330

(1)

 

5820 \; ml

(1)

3. Write 42 \; cm^3 in mm^3

 

(2 marks)

Show answer
42 \times 10^3

(1)

 

42 \ 000

(1)

4. Randeep is going from London to the Belgian town of Bruges.

Randeep will drive from London to Dover.

He will then drive from Calais to Bruges.

The distance from London to Dover is 77.5 \; miles.

The distance from Calais to Bruges is 115 \; km.

 

Use 5 \; miles ≈ 8 \; km

Randeep has enough fuel in her car to drive 140 \; miles.

Does he have enough fuel to get from London to Bruges?

You must show all your working.

 

(3 marks)

Show answer
115\div \frac{8}{5}=71.875

(1)

 

77.5+71.875=149.375

(1)

 

No – Randeep does not have enough fuel.

149.375 is greater than 140 \; miles.

(1)

Learning checklist

You have now learned how to:

  • Choose metric units
  • Convert metric units of length, mass and capacity
  • Convert metric and imperial units
  • Convert units of speed
  • Convert units of area and volume

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