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.