janiya is taking a road trip. the distance she plans to travel can be written as 3 x 10^2 kilometers, 3 x 10^5 meters, 3 x 10^7 centimeters, or 2 x 10^8 millimeters. which distance uses the most appropriate units?

Answer 1

To determine which distance uses the most appropriate units, we need to convert all the distances to the same unit for comparison. Let's convert everything to kilometers:

1. Kilometers: \(3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers}\).

2. Meters:

   • We know that \(1 \text{ kilometer} = 1000 \text{ meters}\).
   • Therefore, \(3 \times 10^5 \text{ meters} = \frac{3 \times 10^5}{1000} \text{ kilometers} = 300 \text{ kilometers}\).

3. Centimeters:

   • We know that \(1 \text{ kilometer} = 100,000 \text{ centimeters}\).
   • Therefore, \(3 \times 10^7 \text{ centimeters} = \frac{3 \times 10^7}{100,000} \text{ kilometers} = 300 \text{ kilometers}\).

4. Millimeters:

   • We know that \(1 \text{ kilometer} = 1,000,000 \text{ millimeters}\).
   • Therefore, \(2 \times 10^8 \text{ millimeters} = \frac{2 \times 10^8}{1,000,000} \text{ kilometers} = 200 \text{ kilometers}\).

Now we summarize:

• \(3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers}\)
• \(3 \times 10^5 \text{ meters} = 300 \text{ kilometers}\)
• \(3 \times 10^7 \text{ centimeters} = 300 \text{ kilometers}\)
• \(2 \times 10^8 \text{ millimeters} = 200 \text{ kilometers}\)

The distances in kilometers, meters, and centimeters all represent the same distance of 300 kilometers, while the distance in millimeters represents a shorter distance of 200 kilometers.

Given these comparisons, the distances expressed in kilometers (either \(3 \times 10^2\) kilometers, \(3 \times 10^5\) meters, or \(3 \times 10^7\) centimeters) are all appropriate for a road trip. However, representing it specifically in kilometers, \(3 \times 10^2\) kilometers, is the most straightforward and appropriate unit for long distances that people typically discuss when planning a road trip.