Express the result of the following calculations to appropriate number of significant figures :

Options

A. `(7.5 xx 206.8)/(0.0512 xx 1002)`
B. 4.20 + 1.6523 + 0.015
C. (1.0042 - 0.0034)(1.23)
D. `(8.5 xx 208.9)/(0.054 xx 9261.6)`

Explanation

To solve the question of expressing the results of calculations to the appropriate number of significant figures, we will follow these steps:

### Step-by-Step Solution:

1. **Identify Significant Figures**:
- Non-zero digits are always significant.
- Any zeros between significant digits are significant.
- Final zeros in a decimal portion are significant.

2. **Perform the Calculations**:
- For each calculation, we will determine the number of significant figures in the numbers involved.

3. **Determine the Least Number of Significant Figures**:
- For multiplication and division, the result should have the same number of significant figures as the number with the least significant figures.
- For addition and subtraction, the result should be rounded to the least number of decimal places.

### Example Calculations:

1. **Calculation 1**: \( \frac{1551}{51.3024} \)
- Significant figures: 1551 has 4 significant figures, 51.3024 has 6 significant figures.
- The result is \( 30.232 \).
- The least number of significant figures is 4 (from 1551), but we round to 2 significant figures: **30**.

2. **Calculation 2**: \( 4.20 + 1.6523 + 0.015 \)
- Significant figures: 4.20 has 2 decimal places, 1.6523 has 4 decimal places, and 0.015 has 3 decimal places.
- The result is \( 5.8673 \).
- Round to the least number of decimal places (2): **5.87**.

3. **Calculation 3**: \( 1.0042 - 0.0034 \)
- Both numbers have 4 decimal places.
- The result is \( 1.0008 \).
- Since both have 4 decimal places, the answer remains: **1.0008**.

4. **Calculation 4**: \( 1.0042 \times 1.23 \)
- Significant figures: 1.0042 has 5 significant figures, 1.23 has 3 significant figures.
- The result is \( 1.2309 \).
- Round to 3 significant figures: **1.23**.

5. **Calculation 5**: \( 8.5 \times 208.9 \times 0.054 \times 9261.6 \)
- Significant figures: 8.5 has 2, 208.9 has 4, 0.054 has 2, and 9261.6 has 5.
- The result is \( 3.5504 \).
- Round to the least significant figures (2): **3.6**.

### Summary of Results:
1. \( \frac{1551}{51.3024} = 30 \)
2. \( 4.20 + 1.6523 + 0.015 = 5.87 \)
3. \( 1.0042 - 0.0034 = 1.0008 \)
4. \( 1.0042 \times 1.23 = 1.23 \)
5. \( 8.5 \times 208.9 \times 0.054 \times 9261.6 = 3.6 \)