Now we need to convert the distance across the U.S. in miles to kilometers. There are 1.6 km in 1 mile. DUS‐km = DUS‐mi · 1.6 km/mile DUS‐km = ？
The Correct Answer and Explanation is:
To convert a distance from miles (DUS-mi) to kilometers (DUS-km), we use the given conversion factor: 1 mile = 1.6 kilometers. This means that for every mile, we multiply by 1.6 to obtain the equivalent distance in kilometers. The conversion formula is:
[
DUS_{\text{km}} = DUS_{\text{mi}} \times 1.6 \, \text{km/mile}
]
Steps to Convert:
- Identify the given distance in miles (DUS-mi): The problem doesn’t provide the exact distance across the U.S. in miles (DUS-mi), so let’s assume the approximate distance is 2,500 miles. This is a common estimate for the distance from the East Coast to the West Coast of the United States.
- Apply the conversion factor: Multiply the given distance in miles by the conversion factor (1.6 km/mile). Using 2,500 miles as an example:
[
DUS_{\text{km}} = 2,500 \, \text{mi} \times 1.6 \, \text{km/mile}
]
[
DUS_{\text{km}} = 4,000 \, \text{km}
]
Thus, the distance across the U.S. is 4,000 kilometers if it is 2,500 miles.
Explanation:
The conversion from miles to kilometers is a linear scaling process, where every mile is equivalent to 1.6 kilometers. This relationship is based on international standards and allows us to switch between the imperial system (miles) and the metric system (kilometers). The reason for multiplying by 1.6 is because 1 mile is defined as exactly 1.609344 kilometers, but for simplicity, it’s commonly rounded to 1.6 in most general conversions.
This method of converting units ensures that measurements are consistent across different systems of measurement. It is especially useful when traveling internationally or working in contexts where the metric system is more widely used, like scientific research, where kilometers are the standard for measuring distances.
To summarize:
- Formula: ( DUS_{\text{km}} = DUS_{\text{mi}} \times 1.6 )
- Example Calculation: For 2,500 miles, the result is 4,000 kilometers.