The document discusses units of measurement in the metric system including prefixes, base units for length, mass and capacity. It provides examples of converting between metric units of length, mass, capacity, area, volume and time. Key details include the prefixes used in the metric system (kilo, centi, milli, micro), base units (metre, gram, litre), and formulas for converting between units (multiplying or dividing by powers of ten).

1. Converting Units of
Measurement
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2. Metric
units
The metric system of measurement is based on powers of
ten and uses the following prefixes:
These prefixes are then followed by a base unit.
The base unit for length is metre.
The base unit for mass is gram.
The base unit for capacity is litre.
Kilo-
Centi-
Milli-
Micro-
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meaning 1000
meaning one hundredth
meaning one thousandth
meaning one millionth

3. Metric units of
length
Metric units used for length are kilometres, metres,
centimetres and millimetres.
1 kilometre (km) =
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1000 metres (m)
1 metre (m) = 100 centimetres (cm)
1 metre (m) = 1000 millimetres (cm)
1 centimetre (cm) = 10 millimetres (cm)

4. Metric units of
length
A race track measures 400 m. An athlete runs
2.6 km around the track. How many laps is this?
400 m = 0.4 km
Number of laps = 2.6 ÷ 0.4
= 6.5 laps
The following day the athlete completes 8 laps.
How many km is this?
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8 laps = 8 × 0.4 km
= 3.2 km

5. Metric units of
mass
Metric units used for mass are tonnes, kilograms and
grams and milligrams.
1 tonne = 1000 kilograms (kg)
1 kilogram (kg) = 1000 grams (g)
1 gram (g) = 1000 milligrams (mg)
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6. Metric units of
mass
60 tea bags weigh 150 g.
How much would 2000 tea bags weigh in kg?
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We can solve this problem using a unitary method.
60 tea bags weigh 150 g
So, 1 tea bag weighs (150 ÷ 60) g = 2.5 g
Therefore, 2000 tea bags weigh (2.5 × 2000) g = 5000 g
= 5 kg

7. Metric units of
capacity
Capacity is a measure of the amount of liquid that a 3-D
object (for example a glass) can hold.
Metric units of capacity are litres (l), centilitres (cl) and
millilitres (ml).
1 litre (l) = 100 centilitres (cl)
1 litre (l) = 1000 millilitres (ml)
1 centilitre (cl) = 10 millilitres (ml)
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8. Metric units of
capacity
A bottle contains 750 ml of orange squash.
The label says: Dilute 1 part squash with 4 parts water.
How many of litres of drink can be made with one bottle?
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If the whole bottle was made up we would have
750 ml of squash + (4 × 750) ml of water
= 750 ml of squash + 3000 ml of water
= 3750 ml of drink
= 3.75 l of drink

9. Converting metric
units
Complete the following:
34 cm =
54.8 cl =
mm 0.0471 km = m
0.4 l = ml 0.3428 m = mm
7.3 kg = g 23.51 g = mg
ml 0.085 m = mm
To convert from a larger metric unit to a smaller
one we need to _
m
_
u
_l_
ti_
p
_
ly
_ by 10, 100, or 1000.
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340
548
47.1
400 342.8
7300 23 510
85

10. Converting metric
units
Complete the following
920 mm =
43.1 cm = m
cm 65800 m = km
530 g = kg 526 mg = g
3460 ml = l 4539 cl = l
87 kg = tonnes
To convert from a smaller metric unit to a larger
one we need to _
d
_
i_
v_
id
_
e
_ by 10, 100, or 1000.
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92
0.431
65.8
0.53 0.526
3.46 45.39
0.087

11. Converting metric
units
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12. Units of
area
How many cm2 are
there in a m2?
1 m × 1 m = 1 m2
So,
1 m2 = 10 000 cm2
1 m2 = 10 000 cm2
1 m
= 100 cm
1 m
= 100 cm
Area is measured in square units.
Here is a square metre or 1 m2.
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100 cm × 100 cm = 1
0
0
0
0
0
0
0
m
c
m
2 2

13. Units of
area
We can use the following to convert between units of area.
1 km2 = 1 000 000 m2
1 hectare = 10 000 m2
1 m2 = 10 000 cm2
1 m2 = 1 000 000 mm2
1 cm2 = 100 mm2
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14. Units of
area
A rectangular field measures 150 m by 250m.
What is the area of the field in hectares?
150 m
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250 m
The area of the field is
150 m × 250 m = 37 500 m2
1 hectare = 100 m × 100 m
= 10 000 m2
37 500 m2 = 3.75 hectares

15. Units of
volume
Volume is measured in cubic units.
Here is a cubic centimetre or 1 cm3.
How many mm3 are
there in a cm3?
1 cm
= 10 mm
1 cm
= 10 mm 1 cm × 1 cm × 1 cm = 1 cm3
So, 1 cm3 = 1000 mm3
1 cm3 = 1000 mm3
1 cm
= 10 mm
10 mm × 10 mm × 10 mm
= 1000 mm3
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16. Units of
volume
Volume is measured in cubic units.
Here is a cubic metre or 1 m3.
How many cm3 are
there in a m3?
1 m
= 100 cm
1 m
= 100 cm 1 m × 1 m × 1 m = 1 m3
So, 1 m3 = 1 000 000 cm3
1 m3 = 1 000 000 cm3
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1 m
= 100 cm
100 cm × 100 cm × 100 cm
= 1 000 000 cm3

17. Units of
volume
We can use the following to convert between units of volume.
1 km3 = 1 000 000 000 m3
1 m3 = 1 000 000 cm3
1 m3 = 1 000 000 000 mm3
1 cm3 = 1000 mm3
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18. Units of
volume
Dice are packed into boxes measuring 20 cm
by 12 cm by 10 cm.
If the dice are 2 cm cubes, how many of them
fit into a box?
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The volume of the box = (20 × 12 × 10) cm3 = 2400 cm3
The volume of one dice = (2 × 2 × 2) cm3 = 8 cm3
Number of dice that fit in the box = 2400 ÷ 8
= 300 dice

19. Volume and
capacity
Capacity is a measure of the amount of liquid that a 3-D
object can hold.
A litre of water, for example, would fill a container
measuring 10 cm by 10 cm by 10 cm (or 1000 cm3)
1 l = 1000 cm3
1 ml = 1 cm3
1000 l = 1 m3
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20. Volume and
capacity
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21. Volume and
capacity
Which holds more juice when full; a litre bottle or
a carton measuring 6 cm by 10 cm by 20 cm?
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The volume of the carton is (6 × 10 × 20) cm3 = 1200 cm3
1 litre = 1000 cm3
The carton holds more juice.

22. Converting units of area, volume and
capacity
Complete the following
3 ha = m2
4000 m2 = ha
2.8 m3 = l 6 200 cm2 = m2
4.35 cm2 = mm2 9.6 cl = cm3
0.07 cm3 = mm3 38 000 cm3 = m3
0.72 l = cm3 5630 cm3 = l
30 000
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0.4
2800 0.62
435 96
70 0.038
720 5.63

23. Units of
time
Time does not use the metric system.
Units of time include years, months, weeks, days, hours (h),
minutes (min) and seconds (s).
1 minute (min) = 60 seconds (s)
1 hour (h) = 60 minutes (min)
1 day = 24 hours (h)
1 week = 7 days
1 year = 365 days = 52 weeks
1 leap year = 366 days
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24. Units of
time
A machine takes 4 minutes and 10 seconds to make a
toy car. How long would it take to make 18 toy cars?
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4 minutes × 18 = 72 minutes
10 seconds × 18 = 180 seconds = 3 minutes
72 minutes + 3 minutes = 75 minutes
= 1 hour 15 minutes

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