Juan is taking a road trip to Pennsylvania. The distance he plans to travel can be written as 2×10^3 kilometers, 2×10^5 meters, 2×10^7 centimeters, or 2×10^8 millimeters. Which answer uses the most appropriate units?

1 answer

To determine the most appropriate units for Juan's road trip to Pennsylvania, we should convert all the given distances to the same unit so we can compare them.

  1. Kilometers: \(2 \times 10^3 \text{ km}\)

    • \(2 \times 10^3 \text{ km} = 2000 \text{ km}\)
  2. Meters: \(2 \times 10^5 \text{ m}\)

    • \(2 \times 10^5 \text{ m} = 200,000 \text{ m}\)
    • To convert meters to kilometers: \(\frac{200,000 \text{ m}}{1000} = 200 \text{ km}\)
  3. Centimeters: \(2 \times 10^7 \text{ cm}\)

    • \(2 \times 10^7 \text{ cm} = 20,000,000 \text{ cm}\)
    • To convert centimeters to kilometers: \(\frac{20,000,000 \text{ cm}}{100,000} = 200 \text{ km}\)
  4. Millimeters: \(2 \times 10^8 \text{ mm}\)

    • \(2 \times 10^8 \text{ mm} = 200,000,000 \text{ mm}\)
    • To convert millimeters to kilometers: \(\frac{200,000,000 \text{ mm}}{1,000,000} = 200 \text{ km}\)

Comparing these distances:

  • Kilometers: 2000 km
  • Meters: 200 km
  • Centimeters: 200 km
  • Millimeters: 200 km

Given that his travel distance is 2000 kilometers, the most appropriate units for describing the distance he plans to travel would be kilometers.

Thus, the answer is 2×10^3 kilometers.