Question

Deacon estimated that a car trip would take 4.5 hours. However, they completed the trip in 5 hours. What is the percent error in their estimation?

Answer 1

To calculate the percent error in Deacon's estimation, we can use the following formula:

\[
\text{Percent Error} = \left( \frac{\text{Absolute Error}}{\text{Exact Value}} \right) \times 100
\]

Where:
- Absolute Error = |Estimated Time - Actual Time|

In this case:
- Estimated Time = 4.5 hours
- Actual Time = 5 hours

First, we calculate the Absolute Error:

\[
\text{Absolute Error} = |4.5 - 5| = | -0.5 | = 0.5 \, \text{hours}
\]

Now we can plug the Absolute Error and Actual Time into the percent error formula:

\[
\text{Percent Error} = \left( \frac{0.5}{5} \right) \times 100
\]

Calculating the fraction:

\[
\frac{0.5}{5} = 0.1
\]

Now, multiply by 100 to find the percent:

\[
0.1 \times 100 = 10
\]

Thus, the percent error in Deacon's estimation is:

\[
\boxed{10\%}
\]