Question
Janiya is taking a road trip distance she plans to travel can be written as 3 times 10^2 kilometers, 3 times 10^5 meters, 3 times 10^7 centimeters or 3 times 10^8 millimeters
Answers
GPT-4o mini
To compare the different distances given in the question, let's first convert all measurements to the same unit, preferably kilometers.
1. **Kilometers**:
- \(3 \times 10^2\) kilometers is already in kilometers.
2. **Meters**:
- To convert meters to kilometers, we use the conversion \(1 \text{ km} = 1000 \text{ m}\).
- \(3 \times 10^5\) meters in kilometers:
\[
\frac{3 \times 10^5 \text{ m}}{1000 \text{ m/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
3. **Centimeters**:
- To convert centimeters to kilometers, we use the conversion \(1 \text{ km} = 100000 \text{ cm}\).
- \(3 \times 10^7\) centimeters in kilometers:
\[
\frac{3 \times 10^7 \text{ cm}}{100000 \text{ cm/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
4. **Millimeters**:
- To convert millimeters to kilometers, we use the conversion \(1 \text{ km} = 1000000 \text{ mm}\).
- \(3 \times 10^8\) millimeters in kilometers:
\[
\frac{3 \times 10^8 \text{ mm}}{1000000 \text{ mm/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
In conclusion, the distance Janiya plans to travel, regardless of the unit used (kilometers, meters, centimeters, or millimeters), is equivalent to \(300 \text{ km}\).
1. **Kilometers**:
- \(3 \times 10^2\) kilometers is already in kilometers.
2. **Meters**:
- To convert meters to kilometers, we use the conversion \(1 \text{ km} = 1000 \text{ m}\).
- \(3 \times 10^5\) meters in kilometers:
\[
\frac{3 \times 10^5 \text{ m}}{1000 \text{ m/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
3. **Centimeters**:
- To convert centimeters to kilometers, we use the conversion \(1 \text{ km} = 100000 \text{ cm}\).
- \(3 \times 10^7\) centimeters in kilometers:
\[
\frac{3 \times 10^7 \text{ cm}}{100000 \text{ cm/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
4. **Millimeters**:
- To convert millimeters to kilometers, we use the conversion \(1 \text{ km} = 1000000 \text{ mm}\).
- \(3 \times 10^8\) millimeters in kilometers:
\[
\frac{3 \times 10^8 \text{ mm}}{1000000 \text{ mm/km}} = 3 \times 10^2 \text{ km} = 300 \text{ km}
\]
In conclusion, the distance Janiya plans to travel, regardless of the unit used (kilometers, meters, centimeters, or millimeters), is equivalent to \(300 \text{ km}\).