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Geometry and Measure - Units of measurement and conversions

Grade 7IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Metric System Prefixes: Understanding kilo (1000), centi (1/100), and milli (1/1000).

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Conversion Rule: Multiply to convert from a larger unit to a smaller unit; Divide to convert from a smaller unit to a larger unit.

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Units of Length: Millimetres (mm), Centimetres (cm), Metres (m), and Kilometres (km).

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Units of Mass: Milligrams (mg), Grams (g), Kilograms (kg), and Tonnes (t).

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Units of Capacity: Millilitres (ml), Centilitres (cl), and Litres (l).

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Square and Cubic Units: Conversion factors for area (units2units^2) and volume (units3units^3) are the linear conversion factors squared or cubed.

📐Formulae

1 cm=10 mm1 \text{ cm} = 10 \text{ mm}

1 m=100 cm1 \text{ m} = 100 \text{ cm}

1 km=1000 m1 \text{ km} = 1000 \text{ m}

1 kg=1000 g1 \text{ kg} = 1000 \text{ g}

1 tonne=1000 kg1 \text{ tonne} = 1000 \text{ kg}

1 litre=1000 ml=1000 cm31 \text{ litre} = 1000 \text{ ml} = 1000 \text{ cm}^3

Area conversion: 1 m2=(100)2 cm2=10,000 cm2\text{Area conversion: } 1 \text{ m}^2 = (100)^2 \text{ cm}^2 = 10,000 \text{ cm}^2

Volume conversion: 1 cm3=(10)3 mm3=1,000 mm3\text{Volume conversion: } 1 \text{ cm}^3 = (10)^3 \text{ mm}^3 = 1,000 \text{ mm}^3

💡Examples

Problem 1:

Convert 4.25 kilometres into metres.

Solution:

4.25×1000=42504.25 \times 1000 = 4250 m

Explanation:

To convert from a larger unit (km) to a smaller unit (m), we multiply by the conversion factor. Since 1 km=1000 m1 \text{ km} = 1000 \text{ m}, we multiply by 1000.

Problem 2:

A bottle contains 750 ml of juice. How many litres is this?

Solution:

750÷1000=0.75750 \div 1000 = 0.75 litres

Explanation:

To convert from a smaller unit (ml) to a larger unit (l), we divide. Since 1000 ml=1 l1000 \text{ ml} = 1 \text{ l}, we divide the value by 1000.

Problem 3:

Convert 5 cm25 \text{ cm}^2 into  mm2\text{ mm}^2.

Solution:

5×102=5×100=500 mm25 \times 10^2 = 5 \times 100 = 500 \text{ mm}^2

Explanation:

Because area is two-dimensional, we must square the linear conversion factor. Since 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}, then 1 cm2=10×10 mm21 \text{ cm}^2 = 10 \times 10 \text{ mm}^2.