Question

Mark estimates that the distance from his house to his school is 15.5 mi. The actual distance is 14.5 mi.

To the nearest tenth of a percent, what is the percent error in Mark's estimate?

Enter your answer in the box.


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Answer 1

To calculate the percent error in Mark's estimate, we can use the following formula:

\[
\text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Actual Value}} \right) \times 100
\]

In this case:

- Estimated Value = 15.5 mi
- Actual Value = 14.5 mi

Now, let's compute the absolute error:

\[
|\text{Estimated Value} - \text{Actual Value}| = |15.5 - 14.5| = 1.0 \text{ mi}
\]

Now we can calculate the percent error:

\[
\text{Percent Error} = \left( \frac{1.0}{14.5} \right) \times 100
\]

Calculating this:

\[
\frac{1.0}{14.5} \approx 0.0689655172
\]

Now multiply by 100 to convert to a percentage:

\[
0.0689655172 \times 100 \approx 6.89655172 \%
\]

Rounding to the nearest tenth of a percent, we get:

\[
\text{Percent Error} \approx 6.9\%
\]

Thus, the percent error in Mark's estimate is:

\[
\boxed{6.9}
\]