To convert the average distance of Venus from the Sun, given in kilometers, to astronomical units (AU), we need to use the given conversion factor.
The given data:
- Distance of Venus from the Sun: 108.2 million kilometers
- Conversion factor: [tex]\(1 \text{ AU} = 1.5 \times 10^8 \text{ km}\)[/tex]
Step-by-Step Solution:
1. Identify the distance in kilometers:
[tex]\[
\text{Distance in km} = 108.2 \times 10^6 \text{ km}
\][/tex]
2. Identify the conversion factor:
[tex]\[
1 \text{ AU} = 1.5 \times 10^8 \text{ km}
\][/tex]
3. Set up the conversion calculation:
To find the distance in astronomical units (AU), divide the distance in kilometers by the conversion factor:
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Conversion factor}}
\][/tex]
4. Perform the calculation:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km}}
\][/tex]
5. Simplify the calculation:
[tex]\[
\text{Distance in AU} = \frac{108.2}{1.5} \times \frac{10^6}{10^8}
\][/tex]
[tex]\[
\text{Distance in AU} = \frac{108.2}{1.5} \times 10^{-2}
\][/tex]
[tex]\[
\text{Distance in AU} = 72.13333333333334 \times 10^{-2}
\][/tex]
[tex]\[
\text{Distance in AU} = 0.7213333333333334 \text{ AU}
\][/tex]
In conclusion, the distance of Venus from the Sun in astronomical units is approximately [tex]\(0.721 \text{ AU}\)[/tex].
Therefore, the closest answer is:
[tex]\[
\boxed{0.72 \text{ AU}}
\][/tex]
So the correct choice is:
[tex]\[
\text{A. } 0.72 \text{ AU}
\][/tex]
