Answer :
Let's solve the problem step-by-step.
1. Identify the given distance and conversion factor:
- The average distance of Venus from the Sun is 108.2 million kilometers (km).
- The conversion factor is given as [tex]\( 1 \, \text{AU} = 1.5 \times 10^8 \, \text{km} \)[/tex].
2. Convert the average distance to Astronomical Units (AU):
We need to convert the distance from kilometers to astronomical units. Using the conversion factor, this involves dividing the distance in kilometers by the conversion factor.
[tex]\[ \text{Distance in AU} = \frac{108.2 \times 10^6 \, \text{km}}{1.5 \times 10^8 \, \text{km/AU}} \][/tex]
3. Simplify the conversion:
- To simplify the fraction, notice both the numerator and the denominator have a factor of [tex]\(10^6\)[/tex] which can be cancelled out:
[tex]\[ \text{Distance in AU} = \frac{108.2}{1.5} \approx 0.7213333333333334 \, \text{AU} \][/tex]
4. Compare the computed result with the given choices:
The given choices are:
- 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]
5. Determine the closest answer:
The computed value [tex]\(0.7213333333333334 \, \text{AU}\)[/tex] is closest to the choice [tex]\(0.72 \, \text{AU}\)[/tex].
Thus, the correct answer is:
A. [tex]\(0.72 \, \text{AU}\)[/tex]
1. Identify the given distance and conversion factor:
- The average distance of Venus from the Sun is 108.2 million kilometers (km).
- The conversion factor is given as [tex]\( 1 \, \text{AU} = 1.5 \times 10^8 \, \text{km} \)[/tex].
2. Convert the average distance to Astronomical Units (AU):
We need to convert the distance from kilometers to astronomical units. Using the conversion factor, this involves dividing the distance in kilometers by the conversion factor.
[tex]\[ \text{Distance in AU} = \frac{108.2 \times 10^6 \, \text{km}}{1.5 \times 10^8 \, \text{km/AU}} \][/tex]
3. Simplify the conversion:
- To simplify the fraction, notice both the numerator and the denominator have a factor of [tex]\(10^6\)[/tex] which can be cancelled out:
[tex]\[ \text{Distance in AU} = \frac{108.2}{1.5} \approx 0.7213333333333334 \, \text{AU} \][/tex]
4. Compare the computed result with the given choices:
The given choices are:
- 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]
5. Determine the closest answer:
The computed value [tex]\(0.7213333333333334 \, \text{AU}\)[/tex] is closest to the choice [tex]\(0.72 \, \text{AU}\)[/tex].
Thus, the correct answer is:
A. [tex]\(0.72 \, \text{AU}\)[/tex]
