Question

Hanson estimated it would take him 6 days to read the latest installment of the Duke's Dragons book series. The new book was longer than Hanson expected, and he actually needed 10 days to read it. What is the percent error for Hanson's estimate?
If necessary, round your answer to the nearest tenth of a percent.
__%

Answer 1

To calculate the percent error of Hanson's estimate, we can use the formula:

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

In this case:
- Actual Value = 10 days (the actual time it took to read the book)
- Estimated Value = 6 days (the time Hanson initially estimated)

Plugging these values into the formula gives:

\[
\text{Percent Error} = \left( \frac{10 - 6}{10} \right) \times 100
\]

Calculating the numerator:

\[
10 - 6 = 4
\]

Now substituting this back into the formula:

\[
\text{Percent Error} = \left( \frac{4}{10} \right) \times 100
\]

Now calculating the fraction:

\[
\frac{4}{10} = 0.4
\]

Now multiplying by 100 to get the percent:

\[
0.4 \times 100 = 40
\]

Thus, the percent error for Hanson's estimate is:

\[
\boxed{40.0\%}
\]