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S8 Measures

Maths Age 14-16

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AS8.1 Converting units

S8 Measures

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Converting units

It is important to be able to convert between a variety of units quickly and accurately.

For example, if we are using a formula to find the volume of an object we must make sure that all the lengths are written using the same units before using the formula.

1) When using a formula

2) When comparing measurementsFor example, suppose one mother gives the weight of her baby in pounds and another mother gives the weight of her baby in kilograms.

We usually use metric units for calculations.

How can we compare the babies’ weights?To compare the weights we convert them to the same unit.

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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.metre.

The base unit for mass is gram.gram.

The base unit for capacity is litre.litre.

Kilo-Centi-Milli-Micro-

meaning one thousandmeaning one hundredthmeaning one thousandthmeaning one millionth

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Metric units of length, mass and capacity

You should know the following metric conversions for length, mass and capacity (liquid volume):

LengthLength

1 km = 1000 m

1 m = 100 cm

1 m = 1000 mm

1 cm = 10 mm

MassMass

1 tonne = 1000 kg

1 kg = 1000 g

1 g = 1000 mg

Capacity and Volume

Capacity and Volume

1 litre = 1000 ml

1 cl = 10 ml

1 m3 = 1000 litres

1 cm3 = 1 ml

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Metric units of area and volume

The metric units for area are mm2, cm2, m2 and km2.

1 m2 = 100 cm × 100 cm

1 m2 = 10,000 cm21 m2 = 10,000 cm2

1 cm2 = 10 mm × 10 mm

1 cm2 = 100 mm21 cm2 = 100 mm2

The metric units for volume are mm3, cm3, m3 and km3.

1 m3 = 100 cm × 100 cm × 100 cm

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

1 cm3 = 10 mm × 10 mm × 10 mm

1 cm3 = 1000 mm31 cm3 = 1000 mm3

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Converting metric units

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

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

For example,

0.43 kg = 0.43 × 1000 g

Convert 0.43 kg to grams

= 430 g

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

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

For example,

7.6 cm = 7.6 ÷ 100 m

Convert 7.6 cm to metres

= 0.076 m

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Converting metric units

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Ordering units

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Imperial units

Imperial units are still frequently used and you should be aware of the following imperial conversions:

1 foot = ___ inches12

1 yard = ___ feet3

1 pound = ___ ounces16

1 stone = ___ pounds14

1 gallon = ___ pints8

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Converting imperial units

We can convert between metric and imperial units using the following approximate conversions:

5 miles is about ___ kilometres8

1 foot is about ___ centimetres30

1 inch is about ___ centimetres2.5

1 kilogram is about ___ pounds2.2

1 gallon is about ___ litres4.5

1 litre is about ____ pints1.75

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Converting imperial units

1 kilogram is about 2.2 pounds.About how many kilograms are there in 1 stone?

1 stone = 14 pounds

Every 2.2 pounds is worth about 1 kilogram. This means that we have to divide 14 pounds by 2.2 to find the equivalent number of kilograms.

14 pounds ≈ 14 ÷ 2.2 kilograms

= 6.4 kilograms

1 stone is about 6.4 kilograms1 stone is about 6.4 kilograms

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Metric and imperial conversions

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