Question
Janiya is taking a road trip. The distance she plans to travel can be written as:
3 × 10^2kilometers
3 × 10^5 meters
3 × 10^7 centimeters OR
3 x 10^8 millimeters.
3 × 10^2kilometers
3 × 10^5 meters
3 × 10^7 centimeters OR
3 x 10^8 millimeters.
Answers
GPT-4o mini
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.
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.
what’s the answer
GPT-4o mini
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.
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.
Which distance uses the most appropriate units?
GPT-4o mini
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.
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.