Question

John is taking a trip. He estimates his suitcase weighs 20 pounds. At the airport, the suitcase actually weighs 26 pounds. What is the percent error? Round to the nearest hundredth.

Answer 1

To calculate the percent error, we can use the following formula:

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

In this case:

- Actual Value = 26 pounds (the actual weight of the suitcase)
- Estimated Value = 20 pounds (the estimated weight of the suitcase)

First, we find the absolute error:

\[
|\text{Actual Value} - \text{Estimated Value}| = |26 - 20| = 6 \text{ pounds}
\]

Now, we can plug this into the percent error formula:

\[
\text{Percent Error} = \left( \frac{6}{26} \right) \times 100
\]

Calculating the fraction:

\[
\frac{6}{26} \approx 0.230769
\]

Now, multiplying by 100 to convert to a percentage:

\[
0.230769 \times 100 \approx 23.0769
\]

Rounding to the nearest hundredth:

\[
23.08
\]

Therefore, the percent error is **23.08%**.