converting unit measures
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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