Let's solve the problem step-by-step.
1. Understand the given data:
- The average distance of Venus from the Sun is [tex]\(108.2\)[/tex] million kilometers.
- The conversion factor is [tex]\(1 \text{ AU} = 1.5 \times 10^8 \text{ km}\)[/tex].
2. Convert the distance from kilometers to astronomical units (AU):
- Given distance in kilometers is [tex]\(108.2 \times 10^6 \text{ km}\)[/tex].
- Conversion factor is [tex]\(1.5 \times 10^8 \text{ km/AU}\)[/tex].
3. Set up the conversion:
To find the distance in AU, we divide the distance in kilometers by the conversion factor.
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km/AU}}
\][/tex]
4. Perform the division:
[tex]\[
\text{Distance in AU} = \frac{108200000}{150000000}
\][/tex]
Simplifying the fraction, we get:
[tex]\[
\text{Distance in AU} \approx 0.7213
\][/tex]
5. Compare with the given options:
- A. 0.72 AU
- B. 1.25 AU
- C. 3.56 AU
- D. 45.63 AU
- E. 96.12 AU
6. Select the closest answer:
The calculated distance is [tex]\(0.7213 \text{ AU}\)[/tex], which is very close to [tex]\(0.72 \text{ AU}\)[/tex].
Hence, the correct answer is:
A. 0.72 AU
