Question

When Destiny agreed to proofread her brother's essay, she expected that it would be 2 pages long. When he gave her the essay, it was actually 4.5 pages long. What is the percent error for her estimate?
If necessary, round your answer to the nearest tenth of a percent.

Answer 1

To calculate the percent error of Destiny'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 = 2 pages
- Actual Value = 4.5 pages

Now we can substitute these values into the formula:

\[
\text{Percent Error} = \left( \frac{2 - 4.5}{4.5} \right) \times 100
\]

Calculating the numerator:

\[
2 - 4.5 = -2.5
\]

Now, substituting back into the formula:

\[
\text{Percent Error} = \left( \frac{-2.5}{4.5} \right) \times 100
\]

Calculating the fraction:

\[
\frac{-2.5}{4.5} \approx -0.5556
\]

Now multiplying by 100:

\[
-0.5556 \times 100 \approx -55.56
\]

Since percent error is expressed in absolute terms, we take the positive value:

\[
\text{Percent Error} \approx 55.6\%
\]

Thus, the percent error for Destiny's estimate is **55.6%**.