If the significant figures are more,

Options

A. percentage error is more and accuracy is less
B. percentage 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 question regarding the relationship between significant figures, percentage error, and accuracy, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding Significant Figures**:
- Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal portion.

2. **Percentage Error Definition**:
- Percentage error is calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{\Delta x}{x} \right) \times 100 \]
- Here, \(\Delta x\) is the absolute error (the least count of the measuring instrument) and \(x\) is the measured value.

3. **Impact of Significant Figures on Percentage Error**:
- When a measurement has more significant figures, it implies that the measurement is more precise. Therefore, the absolute error (\(\Delta x\)) tends to be smaller relative to the measured value (\(x\)).
- This means that as the number of significant figures increases, the percentage error decreases.

4. **Accuracy and Significant Figures**:
- Accuracy refers to how close a measured value is to the true value. More significant figures generally indicate a more accurate measurement because they reflect a finer resolution of the measurement.
- Thus, with more significant figures, the accuracy of the measurement improves.

5. **Evaluating the Options**:
- **Option 1**: Percentage error is more and accuracy is less. (Incorrect)
- **Option 2**: Percentage error is less and accuracy is more. (Correct)
- **Option 3**: Percentage error is less and accuracy is less. (Incorrect)
- **Option 4**: Significant figures show accuracy. (Partially correct but not the best choice)

6. **Conclusion**:
- The correct answer is that with more significant figures, the percentage error is less and the accuracy is more. Therefore, the best option is Option 2.