Sure! Let's break down the process to find the absolute and relative errors.
Step-by-Step Solution:
1. Identify the actual value and the measured value:
- The actual distance to the town is \(\(41.7\)\) miles.
- The measured distance on the odometer is \(\(42.4\)\) miles.
2. Calculate the absolute error:
- The absolute error is the difference between the measured value and the actual value.
- Formula: \(\(|\text{measured value} - \text{actual value}|\)\)
- Plugging in the values: \(\(|42.4 - 41.7|\)\)
- This gives us an absolute error of \(\(0.7\)\) mile(s).
Therefore, the absolute error is \(\(0.7\)\) mile(s).
3. Calculate the relative error:
- The relative error is the absolute error divided by the actual value.
- Formula: \(\(\frac{\text{absolute error}}{\text{actual value}}\)\)
- Plugging in the values: \(\(\frac{0.7}{41.7}\)\)
- This gives us a relative error of approximately \(\(0.017\)\).
Therefore, the relative error is \(\(0.017\)\).
Summary:
- The absolute error is \(\(0.7\)\) mile(s).
- The relative error is \(\(0.017\)\).
