Question

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?

Answer 1

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**.