To convert $0.00405 \, \text{cm}^2$ to $\text{mm}^2$ and $\text{m}^2$, we'll go through each step.

1. Convert cm² to mm²:

Since $1 \, \text{cm} = 10 \, \text{mm}$, the area conversion is: $1 \, \text{cm}^2 = (10 \, \text{mm})^2 = 100 \, \text{mm}^2$

Given: $0.00405 \, \text{cm}^2 \times 100 = 0.405 \, \text{mm}^2$

2. Convert cm² to m²:

Since $1 \, \text{cm} = 0.01 \, \text{m}$, the area conversion is: $1 \, \text{cm}^2 = (0.01 \, \text{m})^2 = 0.0001 \, \text{m}^2$

Given: $0.00405 \, \text{cm}^2 \times 0.0001 = 4.05 \times 10^{-7} \, \text{m}^2$

Summary of conversions:

• To mm²: $0.00405 \, \text{cm}^2 = 0.405 \, \text{mm}^2$
• To m²: $0.00405 \, \text{cm}^2 = 4.05 \times 10^{-7} \, \text{m}^2$

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Relative Questions:

1. How do you convert other units of area like km² to cm²?
2. Why is it necessary to square the conversion factor when converting units of area?
3. How do you convert units of volume, such as cm³ to mm³?
4. What is the difference between converting units of length, area, and volume?
5. How would you convert $0.00405 \, \text{cm}^2$ to $\mu\text{m}^2$?

Tip:

When converting area or volume units, remember to raise the conversion factor to the power corresponding to the dimension (square for area, cube for volume).