To convert the average distance of Venus from the Sun from kilometers to astronomical units (AU), you can follow these detailed steps:
1. Identify the given distance from the Sun to Venus in kilometers.
- Distance from Sun to Venus: 108.2 million kilometers (108.2 × 10^6 km).
2. Identify the conversion factor between kilometers and astronomical units.
- 1 AU = 1.5 × 10^8 km.
3. Use the conversion factor to convert the distance from kilometers to AU. This involves dividing the distance in kilometers by the number of kilometers in one AU.
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in kilometers}}{\text{Conversion factor (km to AU)}}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
\text{Distance in AU} = \frac{108.2 \times 10^6 \text{ km}}{1.5 \times 10^8 \text{ km/AU}}
\][/tex]
5. Perform the division:
- First, calculate the values in the numerator and the denominator:
[tex]\[
\frac{108.2 \times 10^6}{1.5 \times 10^8}
\][/tex]
- Simplify the division:
[tex]\[
\frac{108.2}{150} = 0.7213333333333334
\][/tex]
The calculated distance is approximately 0.7213 AU.
6. Compare the result with the given options and select the closest answer.
- 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 approximate distance of 0.7213 AU is closest to option A, [tex]\(0.72 \, \text{AU}\)[/tex].
Therefore, the closest answer is:
A. [tex]\(0.72 \, \text{AU}\)[/tex]
