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 [tex]\(41.7\)[/tex] miles.
- The measured distance on the odometer is [tex]\(42.4\)[/tex] miles.
2. Calculate the absolute error:
- The absolute error is the difference between the measured value and the actual value.
- Formula: [tex]\(|\text{measured value} - \text{actual value}|\)[/tex]
- Plugging in the values: [tex]\(|42.4 - 41.7|\)[/tex]
- This gives us an absolute error of [tex]\(0.7\)[/tex] mile(s).
Therefore, the absolute error is [tex]\(0.7\)[/tex] mile(s).
3. Calculate the relative error:
- The relative error is the absolute error divided by the actual value.
- Formula: [tex]\(\frac{\text{absolute error}}{\text{actual value}}\)[/tex]
- Plugging in the values: [tex]\(\frac{0.7}{41.7}\)[/tex]
- This gives us a relative error of approximately [tex]\(0.017\)[/tex].
Therefore, the relative error is [tex]\(0.017\)[/tex].
Summary:
- The absolute error is [tex]\(0.7\)[/tex] mile(s).
- The relative error is [tex]\(0.017\)[/tex].
