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Understand Metric Units of Length

In this worksheet, students will convert between different units of length (such as millimetres, centimetres, metres, kilometres, etc.) to find equivalent distances which are identical but are expressed in different ways.

'Understand Metric Units of Length' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

There are a number of units that can be used to describe length, from miles, feet and yards to leagues and metres.

We are going to focus on the most common of these which is the metric measurement metre.

 

All of the metric units you will have heard of are based around the base word 'metre' with other words tacked on to describe their relationship to this unit, e.g.

Kilometre: 'Kilo' means 1000 so 1 km = 1000 m

Centimetre: 'Centi' means 100 so 1 m = 100 cm

Millimetre: 'Milli' means 1000 so 1 m = 1000 mm

 

Another common conversion that is based on these measurements is that 1 cm = 10 mm.

 

 

How to Convert

Step 1: Decide on our conversion factor (i.e. m to km is a conversion of 1000).

Step 2: Either multiply or divide by this number to reach your converted measurement.

 

 

Let's look at this process in an example now.

e.g. Convert 15 cm into metres.

 

Step 1: Decide on our conversion factor.

100cm = 1m so our conversion factor is 100.

 

Step 2: Multiply or divide by this number.

We need to think about this a bit carefully.

The way I look at this is that a metre is bigger than a cm, so there will be less of them overall.

As there is less of them, we need to divide.

15 ÷ 100 = 0.15 m

So 15 cm is the same as 0.15 m.

 

 

 

Let's practise converting in another example now. 

e.g. Convert 1.4 km into metres.

 

Step 1: Decide on our conversion factor.

1000 m = 1 km so our conversion factor is 1000.

 

Step 2: Multiply or divide by this number.

The way I look at this one is that a metre is smaller than a km, so there will be more of them overall.

As there is more of them, we need to multiply.

1.4 x 1000 = 1400 m

So 1.4 km is the same as 1400 m.

 

 

 

In this activity, you will convert between different units of length (such as millimetres, centimetres, metres, kilometres, etc.) to find equivalent distances which are identical but are expressed in different ways. 

How many cm are in 1 metre?

How many metres are in 1 km?

If 15 cm is converted into millimetres, how many millimetres will this be?

1.5 mm

150 mm

1500 mm

If 4.2 km is converted into metres, how many metres will this be?

4200 m

0.0042 m

0.42 m

Select if the following conversions are correct or not.

Select if the following conversions are correct or not.

Match each prefix below to its correct conversion factor in relation to the base word 'metre'. 

Column A

Column B

Kilo-
10 / 1000
Centi-
100
Milli-
1000

Convert 210 mm into cm.

 

Be careful to write only a number with no units, as these have already been written for you. 

Column A

Column B

Kilo-
10 / 1000
Centi-
100
Milli-
1000

Convert 41 m into km.

 

Be careful to write only a number with no units, as these have already been written for you. 

Convert 370 km into m.

 

Be careful to write only a number with no units, as these have already been written for you. 

  • Question 1

How many cm are in 1 metre?

CORRECT ANSWER
100
EDDIE SAYS
The prefix 'centi-' means 100, so there must be 100 cm in a metre. Did you get that one correct? If not, then review the Introduction now before you move on.
  • Question 2

How many metres are in 1 km?

CORRECT ANSWER
1000
EDDIE SAYS
The prefix 'kilo-' means 1000, so there must be 1000 m in a kilometre.
  • Question 3

If 15 cm is converted into millimetres, how many millimetres will this be?

CORRECT ANSWER
150 mm
EDDIE SAYS
We know that to convert between cm and mm, we need to use a conversion factor of 10, as there are 10 mm in 1 cm. The mistake that can be made here is to divide, but we need to multiply. Try to think that millimetres are smaller than centimetres, so there will need to be more of them. In order to create more, we need to multiply: 15 × 10 = 150 mm
  • Question 4

If 4.2 km is converted into metres, how many metres will this be?

CORRECT ANSWER
4200 m
EDDIE SAYS
We know that to convert between km and m, we need to use a conversion factor of 1000, as there are 1000 m in 1 km. It can be helpful to reason that metres are smaller than kilometres, so there will need to be more of them. In order to create more, we need to multiply: 4.2 × 1000 = 4200 mm
  • Question 5

Select if the following conversions are correct or not.

CORRECT ANSWER
EDDIE SAYS
Did you remember to employ the conversions we learnt in our Introduction here? Remember our conversion factors are: mm to cm = 10 m to cm = 100 km to m = 1000 If we check each conversion one-at-a-time, we find that: 3 × 10 = 30 mm so this one is correct; 3.7 × 100 = 370 cm so this is not correct; 3.2 × 1000 = 3200 m so this is also not correct. Were you able to identify the one correct answer shown?
  • Question 6

Select if the following conversions are correct or not.

CORRECT ANSWER
EDDIE SAYS
Here our conversions are getting both larger and smaller, so we will need to employ multiplication and division. If we check each conversion one-at-a-time, we find that: mm > cm uses a conversion factor of × 10 so this one is correct; cm > m uses a conversion factor of ÷ 100 so this one is also correct; m > km uses a conversion factor of ÷ 1000 so this one is incorrect. Were you able to identify these two correct answers?
  • Question 7

Match each prefix below to its correct conversion factor in relation to the base word 'metre'. 

CORRECT ANSWER

Column A

Column B

Kilo-
1000
Centi-
100
Milli-
10 / 1000
EDDIE SAYS
The one that catches people out here is that 'milli-' can create two conversion factors: 1000 if you are converting into m and 10 if you are converting into cm. That's strange, isn't it?! You need to learn this meanings by heart so that you can apply them accurately when converting between units measuring length.
  • Question 8

Convert 210 mm into cm.

 

Be careful to write only a number with no units, as these have already been written for you. 

CORRECT ANSWER
EDDIE SAYS
Did you use the correct conversion factor here? 1 cm = 10 mm Remember that cm are larger than mm, so we need to have less of them. This means we need to divide by our conversion factor. So 210 ÷ 10 = 21 cm
  • Question 9

Convert 41 m into km.

 

Be careful to write only a number with no units, as these have already been written for you. 

CORRECT ANSWER
0.041
EDDIE SAYS
Did you use the correct conversion factor here? 1 km = 1000 m Remember that km are larger than m, so we need to have less of them. This means we need to divide by our conversion factor. So 41 ÷ 1000 = 0.0041 km Did you get on OK with the decimal here? If not, then you can always revise dividing decimals once you have completed this activity.
  • Question 10

Convert 370 km into m.

 

Be careful to write only a number with no units, as these have already been written for you. 

CORRECT ANSWER
370000
EDDIE SAYS
Did you use the correct conversion factor here? 1 km = 1000 m Remember that m are smaller than km, so we need to have more of them. This means we need to multiply by our conversion factor. So 370 × 1000 = 370000 km Well done for completing this activity - you can now convert lengths between different units. Why not try the Level 2 activity using algebraic contexts if you are ready for a challenge?
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