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.
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Miles to Feet: \[ 1 \text{ mile} = 5280 \text{ feet} \] \[ 8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 5280 \text{ feet} \approx 448.8 \text{ feet} \]
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Miles to Inches: \[ 1 \text{ mile} = 63,360 \text{ inches} \] \[ 8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 63,360 \text{ inches} \approx 5391.5 \text{ inches} \]
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Miles to Centimeters: \[ 1 \text{ mile} = 160,934 \text{ centimeters} \] \[ 8.5 \times 10^{-2} \text{ miles} = 8.5 \times 10^{-2} \times 160,934 \text{ centimeters} \approx 1371.7 \text{ centimeters} \]
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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.