Converting standard units

Description

Converting between units means changing a measurement from one unit to another without changing its actual size. For length, mass, and capacity you need to know the key conversion facts.

Key conversions:

• Length: $10\text{ mm} = 1\text{ cm}$, $100\text{ cm} = 1\text{ m}$, $1000\text{ m} = 1\text{ km}$
• Mass: $1000\text{ g} = 1\text{ kg}$, $1000\text{ kg} = 1\text{ tonne}$
• Capacity: $1000\text{ ml} = 1\text{ litre}$

To convert to a smaller unit, multiply. To convert to a larger unit, divide.

$$3.5\text{ km} = 3.5 \times 1000 = 3500\text{ m}$$ $$450\text{ cm} = 450 \div 100 = 4.5\text{ m}$$

Area and volume conversions catch students out. Because area is two-dimensional: $$1\text{ m}^2 = 10000\text{ cm}^2 \quad \text{(not just } 100\text{)}$$

And volume is three-dimensional: $$1\text{ m}^3 = 1,000,000\text{ cm}^3$$

Common error: multiplying by 100 when converting $\text{m}^2$ to $\text{cm}^2$ — you must square the conversion factor.

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