To determine how many astronomical units (AU) the asteroid is from Earth, we need to use the conversion factor between kilometers and astronomical units. One astronomical unit (AU) is defined as the average distance from the Earth to the Sun, which is approximately 149,597,870.7 kilometers.
The distance from Earth to the asteroid is given as 700,000,000 kilometers. To convert this distance to astronomical units, we divide the distance in kilometers by the number of kilometers per astronomical unit.
Let's break it down step-by-step:
1. Given Data:
- Distance from Earth to the asteroid: 700,000,000 kilometers
- Conversion factor: 1 AU ≈ 149,597,870.7 kilometers
2. Set up the conversion:
[tex]\[
\text{Distance in AU} = \frac{\text{Distance in km}}{\text{Kilometers per AU}}
\][/tex]
3. Perform the Division:
[tex]\[
\text{Distance in AU} = \frac{700,000,000 \text{ km}}{149,597,870.7 \text{ km/AU}}
\][/tex]
4. Result:
[tex]\[
\text{Distance in AU} \approx 4.679210985587912
\][/tex]
Since we are looking for an approximation, the distance to the asteroid, about 700,000,000 kilometers, is approximately 4.68 AU. When looking at the given multiple-choice options, the closest value is:
[tex]\[
4.5 \text{ AU}
\][/tex]
Therefore, the asteroid is about 4.5 AU from Earth.
