Understanding and mastering metric units and their conversions are fundamental skills in maths, necessary for solving a wide range of problems in both academic settings and everyday life. This section covers the basics of metric units for length, area, volume, and mass, along with key conversion techniques.

Introduction to Metric Units

The metric system is an international standard based on the number 10. It includes units for length (metres), mass (grams), and volume (litres).

Length Units

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• Millimetre (mm)
• Centimetre (cm): $10 \text{ mm }$
• Metre (m): $100 \text{ cm }$
• Kilometre (km): $1,000 \text { m }$

Area Units

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• Square Millimetre $\text{ mm}^2$
• Square Centimetre $\text{ cm}^2$: $100 \text{ mm}^2$
• Square Metre $\text { m}^2$: $10,000\text { cm}^2$
• Square Kilometre $\text { km}^2$: $1,000,000\text { m}^2$

Volume Units

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• Cubic Millimetre $\text { mm}^3$
• Cubic Centimetre $\text { cm}^3$or Millilitre $\text { ml}$
• Cubic Metre$\text { m}^3$:$1,000,000\text { cm}^3$
• Litre $\text { l}$: $1,000 \text { ml}$

Mass Units

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• Gram $\text { g}$
• Kilogram $\text { kg}$: $1,000\text { g}$

Converting Between Units

Conversion involves multiplying or dividing by 10, 100, or 1,000, depending on the relationship between the units.

Length Conversion Examples

Example 1: Convert 5,000 mm to metres.

• Solution: $5,000 \, \text{mm} \times \frac{1 \, \text{m}}{1,000 \, \text{mm}} = 5 \, \text{m}$

Example 2: Convert 7.5 km to metres.

• Solution: $7.5 \, \text{km} \times \frac{1,000 \, \text{m}}{1 \, \text{km}} = 7,500 \, \text{m}$

Area Conversion Examples

Example 3: Convert 2,000 $\text{cm}^2$ to $\text{m}^2$.

• Solution: $2,000 \, \text{cm}^2 \times \frac{1 \, \text{m}^2}{10,000 \, \text{cm}^2} = 0.2 \, \text{m}^2$

Volume Conversion Examples

Example 4: Convert $1,000,000\text { cm}^3$ to $\text { m}^3$.

• Solution: $1,000,000 \, \text{cm}^3 \times \frac{1 \, \text{m}^3}{1,000,000 \, \text{cm}^3} = 1 \, \text{m}^3$

Mass Conversion Example

Example 5: Convert 2,500 g to kilograms.

• Solution: $2,500 \, \text{g} \times \frac{1 \, \text{kg}}{1,000 \, \text{g}} = 2.5 \, \text{kg}$

Practice Problems

Problem 1: How many millilitres are in 3.5 litres?

Solution:

$3.5 \, \text{l} \times 1,000 \, \text{ml/l} = 3,500 \, \text{ml}$

Problem 2: Convert 9 km to millimetres.

Solution:

$9 \, \text{km} \times \frac{1,000,000 \, \text{mm}}{1 \, \text{km}} = 9,000,000 \, \text{mm}$