To solve these conversions, we'll use the appropriate conversion factors and pay attention to the significant figures.

1. Convert 145 cm² to m²

Conversion factor:
1 m² = 10,000 cm² (since 1 m = 100 cm, then 1 m² = (100 cm)² = 10,000 cm²).

Calculation: $145 \, \text{cm}^2 \times \left(\frac{1 \, \text{m}^2}{10,000 \, \text{cm}^2}\right) = \frac{145}{10,000} \, \text{m}^2 = 0.0145 \, \text{m}^2$

Significant Figures: 145 cm² has 3 significant figures, so the answer should be reported with 3 significant figures.

$\text{Blank 1} = 1.45 \times 10^{-2} \, \text{m}^2 \, \text{(scientific notation)} \, \text{or} \, 0.0145 \, \text{m}^2 \, \text{(standard notation)}$

2. Convert 0.263 m³ to mm³

Conversion factor:
1 m³ = 10^9 mm³ (since 1 m = 1,000 mm, then 1 m³ = (1,000 mm)³ = 10^9 mm³).

Calculation: $0.263 \, \text{m}^3 \times \left(10^9 \, \text{mm}^3\right) = 0.263 \times 10^9 \, \text{mm}^3 = 2.63 \times 10^8 \, \text{mm}^3$

Significant Figures: 0.263 m³ has 3 significant figures, so the answer should be reported with 3 significant figures.

$\text{Blank 2} = 2.63 \times 10^8 \, \text{mm}^3$

Final Answers:

• Blank 1 = $1.45 \times 10^{-2}$ m²
• Blank 2 = $2.63 \times 10^8$ mm³

Would you like more details on any of these conversions or have any questions?

5 Related Questions:

1. How would you convert square meters to square centimeters?
2. What is the significance of significant figures in scientific measurements?
3. How do you convert cubic centimeters to cubic meters?
4. What are the steps to convert square millimeters to square meters?
5. Why is it important to use scientific notation for very large or small numbers?

Tip:

Always make sure that your final answer reflects the correct number of significant figures based on the data provided.