If 97.52 is divided by 2.54, the correct result in terms of significant figures is

Options

A. 38.3937
B. 38.394
C. 65.81
D. 38.4

Explanation

To solve the problem of dividing 97.52 by 2.54 and determining the correct result in terms of significant figures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Numbers and Their Significant Figures**:
- The number 97.52 has **4 significant figures** (all non-zero digits are significant).
- The number 2.54 has **3 significant figures** (again, all non-zero digits are significant).

2. **Perform the Division**:
- Calculate \( \frac{97.52}{2.54} \).
- Performing the calculation gives:
\[ \frac{97.52}{2.54} \approx 38.3937 \]

3. **Determine the Number of Significant Figures for the Result**:
- In division, the result should have the same number of significant figures as the number with the least significant figures used in the calculation.
- Here, the minimum number of significant figures is **3** (from 2.54).

4. **Round the Result to the Correct Number of Significant Figures**:
- The result from the division is 38.3937, which has **6 significant figures**.
- To round this to **3 significant figures**:
- Look at the first three digits: 38.3 (the next digit is 9, which is greater than 5).
- Therefore, we round up the last significant digit (3) to 4.
- Thus, 38.3937 rounded to 3 significant figures is **38.4**.

5. **Final Answer**:
- The correct result of \( \frac{97.52}{2.54} \) in terms of significant figures is **38.4**.

### Summary:
The final answer is **38.4**, which is the result of dividing 97.52 by 2.54 rounded to the correct number of significant figures.

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