To convert the distance from kilometers to astronomical units (AU), we need to use the given conversion factor. Here's the step-by-step process:
1. Identify the given distance and the conversion factor:
- Distance from the Sun to Venus: [tex]\( 108.2 \)[/tex] million kilometers, which can be written as [tex]\( 108.2 \times 10^6 \)[/tex] km.
- Conversion factor: [tex]\( 1 \)[/tex] AU = [tex]\( 1.5 \times 10^8 \)[/tex] km.
2. Convert the distance from kilometers to astronomical units:
- Use the formula:
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Conversion factor}}
\][/tex]
- Plug in the values:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km}}
\][/tex]
3. Calculate the result:
- Simplify the expression:
[tex]\[
\text{Distance in AU} = \frac{108200000 \text{ km}}{150000000 \text{ km}}
\][/tex]
- Perform the division:
[tex]\[
\text{Distance in AU} = 0.7213333333333334
\][/tex]
4. Compare the result to the given answer choices:
The calculated distance in AU is approximately [tex]\( 0.721 \)[/tex]. Among the choices provided:
- A. [tex]\( 0.72 \, \text{AU} \)[/tex]
- B. [tex]\( 1.25 \, \text{AU} \)[/tex]
- C. 355 \, \text{AU}
- D. 45.63 \, \text{AU}
- E. 96.12 \, \text{AU}
The closest answer to [tex]\( 0.721 \)[/tex] is option A: [tex]\( 0.72 \, \text{AU} \)[/tex].
Therefore, the correct answer is [tex]\( \boxed{0.72 \, \text{AU}} \)[/tex].
