To find the distance of Venus in astronomical units (AU) given its distance in kilometers, we will use the provided conversion factor. Here’s the step-by-step process:
### Step 1: Understand the problem
- 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 2: Convert the distance from kilometers to AU
To convert the distance of Venus from kilometers to AU, we divide the distance in kilometers by the conversion factor.
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Conversion factor (km per AU)}}
\][/tex]
Given:
[tex]\[
\text{Distance in kilometers} = 108.2 \times 10^6 \, \text{km}
\][/tex]
[tex]\[
\text{Conversion factor} = 1.5 \times 10^8 \, \text{km/AU}
\][/tex]
Hence, the distance in AU is calculated as:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \, \text{km}}{1.5 \times 10^8 \, \text{km/AU}}
\][/tex]
### Step 3: Perform the division
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6}{1.5 \times 10^8}
\][/tex]
### Step 4: Simplify the calculation
Simplify the given numbers:
[tex]\[
\text{Distance in AU} = \frac{108.2}{150}
\][/tex]
Divide 108.2 by 150:
[tex]\[
\text{Distance in AU} \approx 0.7213333333
\][/tex]
### Step 5: Find the closest option to the calculated distance
From the given choices:
- A. [tex]\(0.72 \, \text{AU}\)[/tex]
- B. [tex]\(1.25 \, \text{AU}\)[/tex]
- C. [tex]\(3.56 \, \text{AU}\)[/tex]
- D. [tex]\(45.63 \, \text{AU}\)[/tex]
- E. [tex]\(96.12 \, \text{AU}\)[/tex]
The closest value to [tex]\(0.7213333333 \, \text{AU}\)[/tex] among the options is [tex]\(0.72 \, \text{AU}\)[/tex].
### Step 6: Conclusion
Thus, the correct answer is:
[tex]\[
\boxed{0.72 \, \text{AU}}
\][/tex]
