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The problem asks for the percentage error in a cyclist's estimate. Here's how to solve it:

1. **Estimated distance**: 80 miles
2. **Actual distance**: 75.5 miles

The formula for percentage error is:

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

Substituting the values:

\[
\text{Percent Error} = \left( \frac{|80 - 75.5|}{75.5} \right) \times 100 = \left( \frac{4.5}{75.5} \right) \times 100 \approx 5.96\%
\]

So, the percent error is approximately **5.96%**.

Would you like more details on how this was solved or have any further questions?

Here are 5 follow-up questions:
1. How is percentage error useful in real-world scenarios?
2. What other situations might require calculating percentage error?
3. How can one minimize percentage error in estimates?
4. Can percentage error be negative?
5. How does this formula change if the actual value is zero?

**Tip**: Always use the absolute value when calculating percentage error to avoid negative results.

A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estimate? Round the percent to the nearest hundredth if necessary.

Learn how to calculate the percentage error for a cyclist's mileage estimate. This problem uses the percent error formula, covering key concepts such as estimation, error measurement, and rounding. Suitable for students in Grades 6-8.

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