If the significant figures are more

Options

A. percentage error is more and accuracy is less
B. percentatge error is less and accuracy is more
C. percentage error is less and accuracy is less
D. percentage error is more and accuracy is more

Answer

To solve the problem regarding significant figures, percentage error, and accuracy, we can break it down into clear steps:

### Step-by-Step Solution:

1. **Understanding Significant Figures**:
- Significant figures are the digits in a number that contribute to its precision. For example, in the number 5.45694, all digits are significant.

2. **Identifying Cases**:
- We will consider two cases for the number 5.45694:
- Case 1: Using **five significant figures** (5.4569)
- Case 2: Using **three significant figures** (5.46)

3. **Rounding Off**:
- For Case 1 (five significant figures), we round the last digit:
- 5.45694 rounds to **5.4569**.
- For Case 2 (three significant figures), we round to:
- 5.45694 rounds to **5.46**.

4. **Calculating the Errors**:
- **Error in Case 1**:
- The original value is 5.45694, and the rounded value is 5.4569.
- The error (Δx) = 5.45694 - 5.4569 = **0.00004**.
- **Error in Case 2**:
- The original value is 5.45694, and the rounded value is 5.46.
- The error (Δx) = 5.45694 - 5.46 = **0.00094**.

5. **Comparing Percentage Errors**:
- **Percentage Error for Case 1**:
- Percentage Error = (Δx / Original Value) * 100
- = (0.00004 / 5.45694) * 100 ≈ **0.000733%**.
- **Percentage Error for Case 2**:
- Percentage Error = (Δx / Original Value) * 100
- = (0.00094 / 5.45694) * 100 ≈ **0.0172%**.

6. **Conclusion**:
- Since the percentage error is smaller when using more significant figures (Case 1), we conclude that:
- **More significant figures lead to less percentage error and higher accuracy**.

### Final Answer:
- Therefore, the answer is that **when more significant figures are used, the percentage error decreases and accuracy increases**.