Question
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Find the absolute and relative errors in the following situation. The actual distance to a certain town is 31.5 miles, but your odometer reads 32.3 miles. The absolute error is \( \square \) mile(s). (Type an integer or decimal rounded to the nearest tenth as needed.)

Ask by Cummings Parry. in the United States
Mar 01,2025

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Answer

The absolute error is 0.8 miles, and the relative error is about 2.5%.

Solution

The absolute error is the difference between the odometer reading and the actual distance. Here, the absolute error is:   Absolute error = 32.3 miles – 31.5 miles = 0.8 miles To find the relative error, we divide the absolute error by the actual distance:   Relative error = 0.8 / 31.5 ≈ 0.0254 This means the relative error is about 2.5% (when expressed as a percentage). So, the absolute error is 0.8 miles, and the relative error is approximately 2.5%.

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The absolute error is found by taking the absolute difference between the actual distance and the measured distance. So, \( |32.3 - 31.5| = 0.8 \) miles. To determine the relative error, we use the formula: \( \frac{\text{Absolute Error}}{\text{Actual Value}} \). Therefore, \( \frac{0.8}{31.5} \approx 0.0254 \). When expressed as a percentage, this is about \( 2.54\% \).

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