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Converting Units of Measurement

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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-

meaning 1000meaning one hundredthmeaning one thousandthmeaning one millionth

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Metric units of length

Metric units used for length are kilometres, metres, centimetres and millimetres.

1 kilometre (km) = 1000 metres (m)

1 metre (m) = 100 centimetres (cm)

1 metre (m) = 1000 millimetres (cm)

1 centimetre (cm) = 10 millimetres (cm)

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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?

8 laps = 8 × 0.4 km

= 3.2 km

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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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Metric units of mass

60 tea bags weigh 150 g.How much would 2000 tea bags weigh in kg?

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

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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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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?

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

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Converting metric units

Complete the following:

34 cm = mm

54.8 cl = ml

0.0471 km = m

0.4 l = ml 0.3428 m = mm

7.3 kg = g 23.51 g = mg

0.085 m = mm

To convert from a larger metric unit to a smaller one we need to _______ by 10, 100, or 1000.multiply

340

548

47.1

400 342.8

7300 23 510

85

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Converting metric units

To convert from a smaller metric unit to a larger one we need to ______ by 10, 100, or 1000.

Complete the following

920 mm = cm

43.1 cm = m

65800 m = km

530 g = kg 526 mg = g

3460 ml = l 4539 cl = l

87 kg = tonnes

divide

92

0.431

65.8

0.53 0.526

3.46 45.39

0.087

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Converting metric units

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Units of area

How many cm2 are there in a m2?

= 100 cm

= 100 cm1 m × 1 m = 1 m2

100 cm × 100 cm = 10000 m2

So,

1 m2 = 10 000 cm21 m2 = 10 000 cm2

1 m

1 m

Area is measured in square units.

Here is a square metre or 1 m2.

10 000 cm2

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Units of area

We can use the following to convert between units of area.

1 km2 = m21 000 000

1 m2 = cm2

1 m2 = mm2

1 cm2 = mm2100

1 hectare = m210 000

10 000

1 000 000

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Units of area

A rectangular field measures 150 m by 250m.What is the area of the field in hectares?

150 m

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

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1 cm

1 cm

1 cm

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?

= 10 mm

= 10 mm 1 cm × 1 cm × 1 cm = 1 cm3

10 mm × 10 mm × 10 mm

So, 1 cm3 = 1000 mm31 cm3 = 1000 mm3

= 10 mm= 1000 mm3

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1 m

1 m

1 m

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?

= 100 cm

= 100 cm 1 m × 1 m × 1 m = 1 m3

100 cm × 100 cm × 100 cm

So, 1 m3 = 1 000 000 cm31 m3 = 1 000 000 cm3

= 100 cm= 1 000 000 cm3

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Units of volume

We can use the following to convert between units of volume.

1 km3 = m31 000 000 000

1 m3 = cm3

1 m3 = mm3

1 cm3 = mm31000

1 000 000

1 000 000 000

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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?

The volume of the box = (20 × 12 × 10) cm3 =

The volume of one dice = (2 × 2 × 2) cm3 = 8 cm3

Number of dice that fit in the box = 2400 ÷ 8

= 300 dice

2400 cm3

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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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Volume and capacity

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Volume and capacity

Which holds more juice when full; a litre bottle or a carton measuring 6 cm by 10 cm by 20 cm?

The volume of the carton is (6 × 10 × 20) cm3 = 1200 cm3

1 litre = 1000 cm3

The carton holds more juice.

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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 0.4

2800 0.62

435 96

70 0.038

720 5.63

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Units of time

Time does not use the metric system.

1 minute (min) = 60 seconds (s)

1 hour (h) = 60 minutes (min)

1 day = 24 hours (h)

1 week = 7 days

Units of time include years, months, weeks, days, hours (h), minutes (min) and seconds (s).

1 year = 365 days = 52 weeks

1 leap year = 366 days

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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?

4 minutes × 18 = 72 minutes

10 seconds × 18 = 180 seconds = 3 minutes

72 minutes + 3 minutes = 75 minutes

= 1 hour 15 minutes