Skill: Convert between metric units of length, area, and volume

Metric prefixes tell you how large a unit is:

• $1\text{ m}=100\text{ cm}$
• $1\text{ km}=1000\text{ m}$
• $1\text{ cm}=10\text{ mm}$

For length, use the conversion factor once. For area, square the factor because there are two dimensions. For volume, cube the factor because there are three dimensions.

Example: Convert:

1. $2.4\text{ m}$ to centimetres
2. $0.35\text{ m}^2$ to square centimetres
3. $1.8\text{ L}$ to cubic centimetres

1. Convert length

Since $1\text{ m}=100\text{ cm}$, multiply by $100$:

$$2.4\text{ m}\times 100=240\text{ cm}$$

So, $2.4\text{ m}=240\text{ cm}$.

2. Convert area

For area, square the length conversion factor:

$$1\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2$$

Now multiply:

$$0.35\text{ m}^2\times 10{,}000=3500\text{ cm}^2$$

So, $0.35\text{ m}^2=3500\text{ cm}^2$.

3. Convert volume

Use the fact that:

$$1\text{ L}=1\text{ dm}^3$$

Also, $1\text{ dm}=10\text{ cm}$, so:

$$1\text{ L}=1\text{ dm}^3=(10\text{ cm})^3=1000\text{ cm}^3$$

Now multiply:

$$1.8\text{ L}\times 1000=1800\text{ cm}^3$$

So, $1.8\text{ L}=1800\text{ cm}^3$.

Remember: use the factor once for length, square it for area, and cube it for volume.