Unit conversion Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Unit conversion questions. See exactly how to solve problems on metric length, mm to cm, cm to mm, m to cm.

metric lengthmm to cmcm to mmm to cmm to kmmm to m

GCSE Foundation70 questionsStep-by-step solutions

Question 1

1 markeasy

Convert

45

mm into centimetres.

Worked solution

Recall the conversion fact
$1\text{ cm} = 10\text{ mm}$
There are 10 millimetres in every centimetre.
Decide whether to multiply or divide
$45 \div 10$
Centimetres are the larger unit, so the number of them must be smaller — divide by 10.
State the answer
$45\text{ mm} = 4.5\text{ cm}$
Check by going back: $4.5 \times 10 = 45$ mm.

Answer

4.5\text{ cm}

Question 2

1 markeasy

Convert

8.6

cm into millimetres.

Worked solution

Recall the conversion fact
$1\text{ cm} = 10\text{ mm}$
Each centimetre is worth 10 millimetres.
Multiply, because millimetres are smaller
$8.6 \times 10 = 86$
Going to a smaller unit makes the number larger.
State the answer
$8.6\text{ cm} = 86\text{ mm}$
Check by going back: $86 \div 10 = 8.6$ cm.

Answer

86\text{ mm}

Question 3

1 markeasy

Convert

0.75

m into centimetres.

Worked solution

Recall the conversion fact
$1\text{ m} = 100\text{ cm}$
There are 100 centimetres in a metre.
Multiply by 100
$0.75 \times 100 = 75$
Centimetres are smaller than metres, so expect a bigger number.
State the answer
$0.75\text{ m} = 75\text{ cm}$
Three quarters of a metre is 75 cm. Check: $75 \div 100 = 0.75$ m.

Answer

75\text{ cm}

Question 4

1 markeasy

Convert

6500

m into kilometres.

Worked solution

Recall the conversion fact
$1\text{ km} = 1000\text{ m}$
A kilometre is 1000 metres.
Divide by 1000
$6500 \div 1000 = 6.5$
Kilometres are the larger unit, so the number gets smaller.
State the answer
$6500\text{ m} = 6.5\text{ km}$
Check: $6.5 \times 1000 = 6500$ m.

Answer

6.5\text{ km}

Question 5

1 markeasy

Convert

250

mm into metres.

Worked solution

Recall the conversion fact
$1\text{ m} = 1000\text{ mm}$
A metre is 100 cm, and each centimetre is 10 mm, so a metre is 1000 mm.
Divide by 1000
$250 \div 1000 = 0.25$
Metres are much larger than millimetres, so the number must shrink.
State the answer
$250\text{ mm} = 0.25\text{ m}$
A quarter of a metre. Check: $0.25 \times 1000 = 250$ mm.

Answer

0.25\text{ m}

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