To convert the distance from kilometers to astronomical units (AU), you can use the given conversion factor: [tex]\( 1 \text{ AU} = 1.5 \times 10^8 \)[/tex] km.
Here are the detailed steps to solve the problem:
1. Identify the given distance: The average distance from Venus to the Sun is 108.2 million kilometers. This can be written as [tex]\( 108.2 \times 10^6 \text{ km} \)[/tex].
2. Identify the conversion factor: We are given that [tex]\( 1 \text{ AU} = 1.5 \times 10^8 \text{ km} \)[/tex].
3. Set up the conversion calculation: We need to convert the distance from kilometers to astronomical units by dividing the distance in kilometers by the number of kilometers per astronomical unit.
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Kilometers per AU}}
\][/tex]
4. Substitute the values into the equation:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km/AU}}
\][/tex]
5. Simplify the calculation:
[tex]\[
\text{Distance in AU} = \frac{108.2}{150}
\][/tex]
6. Perform the division:
[tex]\[
\text{Distance in AU} \approx 0.7213333333333334
\][/tex]
This result is approximately 0.72 when rounded to two decimal places. Therefore, the correct answer is:
A. [tex]\( 0.72 \text{ AU} \)[/tex]
