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

1. Multiplication: $8.957 \, \text{cm} \times 4.165 \, \text{cm} \times 12.532 \, \text{cm}$

• Calculation: $8.957 \times 4.165 \times 12.532 = 467.6119571 \, \text{cm}^3$
• Significant Figures:
  • $8.957$ has 4 significant figures.
  • $4.165$ has 4 significant figures.
  • $12.532$ has 5 significant figures.
  • The result should be rounded to the least number of significant figures, which is 4.
• Final Answer: $467.6 \, \text{cm}^3$

2. Addition: $17.0 \, \text{g} + 5.079 \, \text{g} + 0.0230 \, \text{g}$

• Calculation: $17.0 + 5.079 + 0.0230 = 22.102 \, \text{g}$
• Significant Figures:
  • $17.0$ has 3 significant figures (1 decimal place).
  • $5.079$ has 4 significant figures (3 decimal places).
  • $0.0230$ has 3 significant figures (4 decimal places).
  • The result should be rounded to the least number of decimal places, which is 1.
• Final Answer: $22.1 \, \text{g}$

3. Division: $\frac{88.5 - 87.57}{45.13}$

• Subtraction: $88.5 - 87.57 = 0.93$
  • $88.5$ has 3 significant figures (1 decimal place).
  • $87.57$ has 4 significant figures (2 decimal places).
  • The result $0.93$ should be rounded to 2 significant figures (1 decimal place).
• Division: $\frac{0.93}{45.13} = 0.020605502 \approx 0.0206$
• Significant Figures:
  • $0.93$ has 2 significant figures.
  • $45.13$ has 4 significant figures.
  • The final result should have 2 significant figures.
• Final Answer: $0.0206$

Summary of Results

1. $8.957 \times 4.165 \times 12.532 = 467.6 \, \text{cm}^3$
2. $17.0 + 5.079 + 0.0230 = 22.1 \, \text{g}$
3. $\frac{88.5 - 87.57}{45.13} = 0.0206$

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

Here are five questions related to this topic:

1. What are the rules for determining significant figures in multiplication?
2. How do significant figures affect the precision of your results?
3. Can you explain why addition and subtraction have different rules for significant figures compared to multiplication and division?
4. How do you determine the number of significant figures when performing multiple operations?
5. What is the difference between precision and accuracy in measurements?

Tip: Always start by identifying the number of significant figures in each value before performing calculations to ensure the final answer is accurate and precise.