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Select the correct answer.

Venus is an average distance of 108.2 million kilometers from the Sun. Use the conversion factor [tex]1 \, \text{AU} = 1.5 \times 10^8 \, \text{km}[/tex] to convert this distance from kilometers to astronomical units. Choose 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]



Answer :

GinnyAnswer
Let's work through the problem step by step to find the distance of Venus from the Sun in astronomical units (AU).

1. Given Data:
- Distance from Venus to the Sun: [tex]\(108.2 \text{ million kilometers}\)[/tex]
- Conversion factor: [tex]\(1 \text{ AU} = 1.5 \times 10^8 \text{ kilometers}\)[/tex]

2. Express the distance from Venus to the Sun in standard form:
- [tex]\(108.2 \text{ million kilometers}\)[/tex] is equal to [tex]\(108.2 \times 10^6 \text{ kilometers}\)[/tex].

3. Set up the conversion:
- We need to convert the distance from kilometers to astronomical units using the given conversion factor.
- Formula: [tex]\[ \text{Distance in AU} = \frac{\text{Distance in kilometers}}{\text{Conversion factor}} \][/tex]

4. Substitute the values:
- [tex]\[ \text{Distance in AU} = \frac{108.2 \times 10^6 \text{ kilometers}}{1.5 \times 10^8 \text{ kilometers}} \][/tex]

5. Perform the division:
- Simplify the expression: [tex]\[ \text{Distance in AU} = \frac{108.2}{150} \][/tex]

6. Calculation result:
- [tex]\[ \text{Distance in AU} = 0.7213 \][/tex]

The closest answer to [tex]\(0.7213 \text{ AU}\)[/tex] is:

A. [tex]\(0.72 \text{ AU}\)[/tex]