Juan is taking a road trip to Pennsylvania. the distance he plans to travel can be written as 2x10^3 kilometers, 2x10^5 meters, 2x10^7 centimeters, or 2x10^8 millimeters. Which answer uses the most appropriate units?

Answer 1

To determine which representation of the distance Juan plans to travel is most appropriate, we should consider the magnitude of the distance in relation to the common units of distance.

Let's convert each of the given distances to kilometers to compare them:

1. Kilometers:

   • \(2 \times 10^3\) kilometers is \(2000\) kilometers.

2. Meters:

   • \(2 \times 10^5\) meters is converted to kilometers by dividing by \(1000\): \[ \frac{2 \times 10^5}{1000} = 200 \text{ kilometers.} \]

3. Centimeters:

   • \(2 \times 10^7\) centimeters is converted to kilometers by dividing by \(100,000\) (since \(100,000\) centimeters = \(1\) kilometer): \[ \frac{2 \times 10^7}{100000} = 200 \text{ kilometers.} \]

4. Millimeters:

   • \(2 \times 10^8\) millimeters is converted to kilometers by dividing by \(1,000,000\) (since \(1,000,000\) millimeters = \(1\) kilometer): \[ \frac{2 \times 10^8}{1000000} = 200 \text{ kilometers.} \]

Now, let's summarize the distances in kilometers:

• \(2 \times 10^3\) kilometers = \(2000\) kilometers
• \(2 \times 10^5\) meters = \(200\) kilometers
• \(2 \times 10^7\) centimeters = \(200\) kilometers
• \(2 \times 10^8\) millimeters = \(200\) kilometers

The distance of \(2000\) kilometers (as written in kilometers) is the largest, which is appropriate for road trip distances since it matches typical travel ranges.

Thus, the answer that uses the most appropriate units is:

2 x 10^3 kilometers.