Let's perform each calculation and determine the correct number of significant figures for each result.

1. Multiplication: $22.87 \, \text{cm} \times 3.45 \, \text{cm} \times 11.446 \, \text{cm}$

• Calculation: $22.87 \times 3.45 \times 11.446 = 902.278251 \, \text{cm}^3$
• Significant Figures:
  • $22.87$ has 4 significant figures.
  • $3.45$ has 3 significant figures.
  • $11.446$ has 5 significant figures.
  • The result should be rounded to the least number of significant figures, which is 3.
• Final Answer: $902 \, \text{cm}^3$

Correct Option: $903 \, \text{cm}^3$

2. Addition: $0.147 \, \text{g} + 0.00663 \, \text{g} + 0.0122 \, \text{g}$

• Calculation: $0.147 + 0.00663 + 0.0122 = 0.16583 \, \text{g}$
• Significant Figures:
  • $0.147$ has 3 significant figures (3 decimal places).
  • $0.00663$ has 3 significant figures (5 decimal places).
  • $0.0122$ has 3 significant figures (4 decimal places).
  • The result should be rounded to the least number of decimal places, which is 3.
• Final Answer: $0.166 \, \text{g}$

Correct Option: $0.166 \, \text{g}$

3. Division: $\frac{73.58 - 22.6}{9.412}$

• Subtraction: $73.58 - 22.6 = 50.98$
  • $73.58$ has 4 significant figures (2 decimal places).
  • $22.6$ has 3 significant figures (1 decimal place).
  • The result $50.98$ should be rounded to 3 significant figures (1 decimal place).
• Division: $\frac{50.98}{9.412} = 5.4183 \approx 5.42$
• Significant Figures:
  • $50.98$ has 3 significant figures.
  • $9.412$ has 4 significant figures.
  • The final result should have 3 significant figures.
• Final Answer: $5.42$

Correct Option: $5.42$

Summary of Results

1. $22.87 \times 3.45 \times 11.446 = 903 \, \text{cm}^3$
2. $0.147 + 0.00663 + 0.0122 = 0.166 \, \text{g}$
3. $\frac{73.58 - 22.6}{9.412} = 5.42$

Would you like further details or have any questions about these calculations?

Here are five questions related to this topic:

1. What is the significance of rounding in scientific calculations?
2. How do you determine the correct number of significant figures in a result?
3. Why is it important to maintain consistency in significant figures across calculations?
4. What are the rules for significant figures when dealing with subtraction and division?
5. How would errors in rounding affect the accuracy of the final result?

Tip: When performing calculations, always consider the operation's effect on significant figures to ensure the precision and accuracy of your results.