A home run hit in a professional baseball game was measured to have traveled a distance of 8.5×10−2 miles.

To determine the most appropriate unit of measurement for a home run distance of \( 8.5 \times 10^{-2} \) miles, we can convert this distance into feet, inches, centimeters, and kilometers to see which is most suitable for expressing such a distance in a baseball context.

1. **Miles to Feet**:
\[
1 \text{ mile} = 5280 \text{ feet}
\]
\[
8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 5280 \text{ feet} \approx 448.8 \text{ feet}
\]

2. **Miles to Inches**:
\[
1 \text{ mile} = 63,360 \text{ inches}
\]
\[
8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 63,360 \text{ inches} \approx 5391.5 \text{ inches}
\]

3. **Miles to Centimeters**:
\[
1 \text{ mile} = 160,934 \text{ centimeters}
\]
\[
8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 160,934 \text{ centimeters} \approx 1371.7 \text{ centimeters}
\]

4. **Miles to Kilometers**:
\[
1 \text{ mile} \approx 1.60934 \text{ kilometers}
\]
\[
8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 1.60934 \text{ kilometers} \approx 0.136 \text{ kilometers}
\]

Based on these conversions:
- **Feet (approximately 448.8 feet)** is the most common and appropriate unit used in baseball for measuring distances such as homerun distances.
- **Inches** (about 5391.5 inches) and **centimeters** (about 1371.7 cm) are less common for this application.
- **Kilometers** (approximately 0.136 km) is too large a unit for such a short distance in a baseball context.

Thus, the most appropriate unit of measurement to describe the distance of a home run in this case is **feet**.