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

Answer 1

To determine which distance uses the most appropriate units, we should convert all the distances to a common unit for comparison. Let's convert them to kilometers:

1. Kilometers:

   • \(3 \times 10^2\) kilometers = 300 kilometers.

2. Meters:

   • \(3 \times 10^5\) meters = \(3 \times 10^5\) meters \(\div 1000 = 300\) kilometers.

3. Centimeters:

   • \(3 \times 10^5\) centimeters = \(3 \times 10^5\) centimeters \(\div 100,000 = 3\) kilometers.

4. Millimeters:

   • \(3 \times 10^8\) millimeters = \(3 \times 10^8\) millimeters \(\div 1,000,000 = 300\) kilometers.

Now we have:

• 300 kilometers (from kilometers)
• 300 kilometers (from meters)
• 3 kilometers (from centimeters)
• 300 kilometers (from millimeters)

Out of these, the distances expressed in kilometers (3 × 10^2 km, 3 × 10^5 m, and 3 × 10^8 mm) are all equivalent at 300 kilometers. The distance expressed in centimeters (3 × 10^5 cm) is significantly smaller at only 3 kilometers.

Since Janiya is on a road trip and the majority of the distances (300 km) are appropriate for travel, the distance of 3 × 10^2 kilometers is the most appropriate unit for her road trip planning. It clearly conveys the distance in a commonly used unit for road travel.