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

To convert metric units, first find the conversion factor between the units. Then use that factor:

• Length: use the factor once.
  $1\text{ m}=100\text{ cm}$
• Area: square the factor.
  $1\text{ m}^2=(100\text{ cm})^2=10{,}000\text{ cm}^2$
• Volume: cube the factor.
  $1\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3$

The unit label helps you remember whether to use the factor once, twice, or three times.

Example: Convert $0.04\text{ m}^3$ to cubic centimeters.

Since this is a volume conversion, cube the length conversion factor.

1. Start with the basic length relationship:

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

2. Cube both sides:

$$1\text{ m}^3=(100\text{ cm})^3=1{,}000{,}000\text{ cm}^3$$

3. Multiply by $0.04$:

$$0.04\text{ m}^3\times 1{,}000{,}000 =40{,}000\text{ cm}^3$$

Therefore,

$$\boxed{0.04\text{ m}^3=40{,}000\text{ cm}^3}$$

For comparison, liters and milliliters use the relationship $1\text{ L}=1{,}000\text{ mL}$. Always check the unit type before converting: length, area, and volume use different powers of the conversion factor.