By using a conversion factor from the back inside cover, determine the length in kilometers of a 500.0-mi automobile race.
The correct answer and explanation is:
To convert 500.0 miles to kilometers, you need to use the appropriate conversion factor between miles and kilometers. From the conversion factor on the back inside cover, you can find that:
1 mile = 1.60934 kilometers.
Now, to convert miles to kilometers, multiply the number of miles by the conversion factor.
For this specific problem, the calculation is as follows: 500.0 miles×1.60934 km/mile=804.672 km500.0 \, \text{miles} \times 1.60934 \, \text{km/mile} = 804.672 \, \text{km}
Thus, the length of the 500.0-mile automobile race is approximately 804.7 kilometers.
Explanation:
- Conversion Factor: The conversion factor tells us how one unit (mile) relates to another unit (kilometer). In this case, for every 1 mile, there are 1.60934 kilometers. This relationship comes from the standard conversion used for geographic distances.
- Setting up the Equation: To convert miles to kilometers, we multiply the distance in miles (500.0 miles) by the conversion factor (1.60934 km per mile).
- Calculating the Result: The multiplication gives 804.672 km, which is rounded to 804.7 km for simplicity.
Why the Conversion is Important:
Conversions like this are commonly used when comparing distances in different units. The United States, for example, still primarily uses miles for road distances, while many other countries and scientific fields use kilometers. Understanding how to convert between units accurately is essential for international travel, scientific research, and engineering applications.