3.17 The answer to the calculation below should be reported to how many significant figures? (97+19.5)/434.97= [1] A. 2 B. 5 C. 4 D. 3

To determine how many significant figures the answer to the calculation \(\frac{97 + 19.5}{434.97}\) should be reported to, we need to follow these steps:

1. **Addition/Subtraction Rule:** When adding or subtracting numbers, the result should have as many decimal places as the number with the fewest decimal places.
   - \(97\) has 0 decimal places.
   - \(19.5\) has 1 decimal place.
   - Therefore, the result of \(97 + 19.5 = 116.5\) should have 1 decimal place.

2. **Division Rule:** When dividing numbers, the result should have as many significant figures as the number with the fewest significant figures.
   - The numerator \(116.5\) (after addition) has 4 significant figures.
   - The denominator \(434.97\) has 5 significant figures.
   - The result should be reported to the number of significant figures of the numerator, which is 4.

Thus, the correct answer is:

**C. 4**

Would you like any further details or have any questions?

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**Related Questions:**

1. How do you determine the significant figures in a sum or difference?
2. Why does division consider the fewest significant figures for reporting results?
3. What is the difference between significant figures in multiplication and division versus addition and subtraction?
4. How do rounding rules affect significant figures in scientific calculations?
5. Can you provide examples of different operations with significant figures?

**Tip:** Always remember that the significant figures of a result are dictated by the least precise measurement used in the calculation.

Explore how to determine significant figures in arithmetic calculations with a detailed explanation of addition and division rules. This problem focuses on adding numbers with different decimal places and dividing to the least number of significant figures. Suitable for high school students studying scientific notation and precision in calculations.

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