Janiya is taking a road trip. The distance she plans to travel can be written as:

Question

3 × 10^2kilometers
3 × 10^5 meters
3 × 10^7 centimeters OR
3 x 10^8 millimeters.

Answer 1

To determine whether Janiya's planned travel distance is consistent across the various units of measurement, we'll convert each distance into a common unit, such as kilometers.

1. Kilometers:
   The distance is already given as \(3 \times 10^2\) kilometers, which is 300 kilometers.

2. Meters:
   To convert meters to kilometers, we divide by 1,000 (since 1 kilometer = 1,000 meters).
   \[ 3 \times 10^5 \text{ meters} = \frac{3 \times 10^5}{10^3} \text{ kilometers} = 3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers} \]

3. Centimeters:
   To convert centimeters to kilometers, we divide by 100,000 (since 1 kilometer = 100,000 centimeters).
   \[ 3 \times 10^7 \text{ centimeters} = \frac{3 \times 10^7}{10^5} \text{ kilometers} = 3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers} \]

4. Millimeters:
   To convert millimeters to kilometers, we divide by 1,000,000 (since 1 kilometer = 1,000,000 millimeters).
   \[ 3 \times 10^8 \text{ millimeters} = \frac{3 \times 10^8}{10^6} \text{ kilometers} = 3 \times 10^2 \text{ kilometers} = 300 \text{ kilometers} \]

In all conversions, the distances match at 300 kilometers. Therefore, Janiya's planned travel distance can be accurately expressed in any of the provided forms.

Answer 2

what’s the answer

Answer 3

The answer is that all the distance expressions Janiya is considering represent the same travel distance of 300 kilometers:

1. \(3 \times 10^2\) kilometers = 300 kilometers
2. \(3 \times 10^5\) meters = 300 kilometers
3. \(3 \times 10^7\) centimeters = 300 kilometers
4. \(3 \times 10^8\) millimeters = 300 kilometers

So, she can use any of these representations, as they all are equivalent to 300 kilometers.

Answer 4

Which distance uses the most appropriate units?

Answer 5

The most appropriate unit for Janiya's road trip distance would be kilometers.

Here’s why:

• Kilometers are commonly used for measuring longer distances such as those encountered on road trips, making it easy to understand and communicate the distance traveled.
• Meters, while directly converting to kilometers, are generally used for shorter distances and might not be as practical for road trips.
• Centimeters and millimeters are typically used for measuring shorter lengths (e.g., height, width) and are not suitable for the context of a road trip.

Thus, expressing the distance as 3 × 10² kilometers is the most suitable choice for clarity and relevance to the task of traveling by road.