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:
\[ \boxed{10%} \]