GCSE Maths Ratio and Proportion

Units of Measurement

Converting Metric Units

Converting Metric Units

Here we will learn about converting metric units, including metric units of length, metric units of mass and metric units of capacity (volume).

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

What is converting metric units?

Converting metric units is being able to convert between different metric units of length, mass or volume.

To do this we need to know what the metric units are and their conversion factors.

We can use prefixes to make these metric units bigger and smaller.

The main ones used are kilo, centi and milli:

Converting metric units Image 1

What is converting metric units?

What is converting metric units?

Metric units of length

The SI unit (international system of units) of length is the metre (m) .

For length we mostly use kilometres (km) , metres (m) , centimetres (cm) and millimetres (mm) .

1 \ km=1000 \ m

1 \ m= 100 \ cm

1 \ m= 1000 \ mm

1 \ cm= 10 \ mm

Converting metric units Image 2

E.g.

Covert 7 \ m to centimetres

7 \times 100=700

So, 7 \ m=700 \ cm

Metric units of mass

The metric system for mass is based around grams (g) .

For mass we mostly use tonnes (t) , kilograms (kg) , and grams (g) .

1 \ tonne=1000 \ kg

1 \ kg= 1000 \ g

Converting metric units Image 3

E.g.

Covert 4 \ kg to centimto grams

4 \times 1000=4000

So, 4 \ kg=4000 \ g

Metric units of capacity (volume)

The SI unit The metric system for capacity is based on litres (l) .

For volume we mostly use litres (l) , centilites (cl) , and millilitres (ml) .

1 \ litre=1000 \ ml

1 \ litre= 100 \ cl

1 \ cl= 10 \ ml

We also need to be aware that:

1 \ litre=1000 \ cm^3

Converting metric units Image 4

E.g.

Covert 6000 \ ml to litres

6000 \div 1000 = 6

So, 6000 \ ml=6 \ l

How to convert metric units

In order to convert metric units:

  1. Find the unit conversion.
  2. Multiply or divide.
  3. Write the answer.

How to convert metric units

How to convert metric units

Converting metric units worksheet

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

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Converting metric units worksheet

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

COMING SOON

Converting metric units examples

Example 1: converting length

Convert 3.2 \ m to cm

  1. Find the unit conversion.

1 \ m=100 \ cm

2Multiply or divide.

As we are going from larger units to smaller units we multiply.

3.2 \times 100=320

3Write the answer.

3.2 \ m=320 \ cm

Example 2: converting length

Convert 780 \ mm to cm

1 \ cm=10 \ mm

As we are going from smaller units to larger units we divide.


780 \div 10=78

780 \ mm=78 \ cm

Example 3: converting mass

Convert 12.5 \ kg to g

1 \ kg=1000 \ g

As we are going from larger units to smaller units we multiply.


12.5 \times 1000=12 \ 500

12.5 \ kg=12 \ 500 \ g

Example 4: converting mass

Convert 3800 \ g to kg

1 \ kg=1000 \ g

As we are going from smaller units to larger units we divide.


3800\div 1000=3.8

3800 \ g=3.8 \ kg

Example 5: converting capacity

Convert 7.1 \ l to ml

1 \ l=1000 \ ml

As we are going from larger units to smaller units we multiply.


7.1 \times 1000=7100

7.1 \ l=7100 \ ml

Example 6: converting capacity

Convert 750 \ ml to l

1 \ l=1000 \ ml

As we are going from smaller units to larger units we divide.


750 \div 1000=0.75

750 \ ml=0.75 \ l

Example 7: converting capacity

Convert 6.8 \ l to cm^3

1 \ l=1000 \ cm^3

As we are going from larger units to smaller units we multiply.


6.8 \times 1000=6800

6.8 \ l=6800 \ cm^3

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

Practice converting metric units questions

1. Convert:  390 \ cm to m

39 \ m
GCSE Quiz False

3.9 \ m
GCSE Quiz True

390 \ m
GCSE Quiz False

0.39 \ m
GCSE Quiz False

Converting centimetres to metres we divide by 100 .

 

390\div 100=3.9 \ m

2. Convert:    57 \ cm to mm

5 \ 700 \ mm
GCSE Quiz False

5.7 \ mm
GCSE Quiz False

570 \ mm
GCSE Quiz True

57 \ 000 \ mm
GCSE Quiz False

Converting centimetres to millimetres we multiply by 10 .

 

57\times 10=570 \ cm

3. Convert:    81 \ 000 \ g to kg

810 \ kg
GCSE Quiz False

81 \ kg
GCSE Quiz True

8.1 \ kg
GCSE Quiz False

8100 \ kg
GCSE Quiz False

Converting grams to kilograms we divide by 1000 .

 

81\ 000\div 1000=81 \ kg

4. Convert:    630 \ kg to tonnes

6300 \ tonnes
GCSE Quiz False

6.3 \ tonnes
GCSE Quiz False

63 \ tonnes
GCSE Quiz False

0.63 \ tonnes
GCSE Quiz True

Converting kilograms to tonnes we divide by 1000 .

 

630\div 1000=0.63 \ tonnes

5. Convert:    4.8 \ l to ml

4800 \ ml
GCSE Quiz True

480 \ ml
GCSE Quiz False

48 \ ml
GCSE Quiz False

48 \ 000 \ ml
GCSE Quiz False

Converting litres to millilitres we multiply by 1000 .

 

4.8\times 1000=4800 \ ml

6. Convert:    560 \ ml to l

56 \ l
GCSE Quiz False

0.56 \ l
GCSE Quiz True

5.6 \ l
GCSE Quiz False

0.056 \ l
GCSE Quiz False

Converting millilitres to litres we divide by 1000 .

 

560\div 1000=0.56 \ l

Converting metric units GCSE questions

1. Write 376 \ cm in metres.

 

(1 mark)

Show answer
376\div 100=3.76

(1)

2. Here is a signpost

 

Converting metric units GCSE question 2

 

How far apart are the Town Centre and the Park?

Give your answer in kilometres.

 

(3 marks)

Show answer
650\div 1000 = 0.65

Converting distance to km

(1)

 

3.5+0.65

Adding the two distances

(1)

 

4.15 \ km

(1)

3. A bottle contains 1.75 litres of lemonade.

A can contains 330 \ ml of lemonade.

 

Phil has 2 bottles of lemonade and 6 cans of lemonade.

How much lemonade does he have in total?

Give your answer in millilitres.

 

(3 marks)

Show answer
1.75\times 1000=1750

Converting capacity to millilitres

(1)

 

2\times 1750+6\times 330

For finding the total

(1)

 

5480 \ ml

(1)

4.  4 tins of soup have a mass of 1.8kg.

3 tins of soup and 2 packets of soup have a mass of 1420 \ g.

 

Find the mass of 7 tins of soup and 5 packets of soup.

Give your answer in kilograms.

 

(5 marks)

Show answer
1.8\div4=0.45 \ kg

Finding the mass of one tin

(1)

 

1420\div 1000=1.42 \ kg

Converting mass to kg

(1)

 

(1.42-3\times 0.45)\div 2=0.035

(1)

 

7\times 0.45+5\times 0.035

(1)

 

3.325 \ kg

(1)

Learning checklist

You have now learned how to:

  • Convert metric units of length
  • Convert metric units of mass
  • Convert metric units of capacity (volume)

The next lessons are

  • Converting units (including the imperial system)
  • Converting units of area and volume

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