What is the advantage gained by using tools with less uncertainty? (Hint: use \% error calculated to support your answer.)

To understand the advantage gained by using tools with less uncertainty, we can analyze the concept of percentage error, which is a common way to express the accuracy of measurements. The percentage error is calculated using the formula: \[ \text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{True Value}} \right) \times 100 \] Where: - Absolute Error is the difference between the measured value and the true value. - True Value is the actual value that is being measured. ### Step-by-Step Explanation: 1. **Understanding Absolute Error**: - Absolute error quantifies how far off a measurement is from the true value. A smaller absolute error indicates a more accurate measurement. 2. **Calculating Percentage Error**: - The percentage error gives a relative measure of the error in relation to the true value. It allows for comparison between different measurements or tools, regardless of the scale of the values being measured. 3. **Impact of Tool Uncertainty**: - Tools with less uncertainty typically have smaller absolute errors. This means that when using such tools, the absolute error will be lower, leading to a lower percentage error. 4. **Example Calculation**: - Suppose we have a true value of \( T = 100 \). - If Tool A has an absolute error of \( 2 \), the percentage error would be: \[ \text{Percentage Error}_A = \left( \frac{2}{100} \right) \times 100 = 2\% \] - If Tool B has an absolute error of \( 5 \), the percentage error would be: \[ \text{Percentage Error}_B = \left( \frac{5}{100} \right) \times 100 = 5\% \] 5. **Conclusion**: - From the calculations, Tool A, which has less uncertainty, results in a lower percentage error (2%) compared to Tool B (5%). This indicates that measurements taken with Tool A are more reliable and accurate. - Therefore, the advantage of using tools with less uncertainty is that they provide more accurate measurements, which is crucial in scientific experiments, engineering applications, and any field where precision is important. In summary, using tools with less uncertainty leads to lower percentage errors, enhancing the reliability and accuracy of measurements.