Answer :
To determine the distance of the asteroid from Earth in astronomical units (AU) given that it is 700,000,000 kilometers away, we need to know that 1 astronomical unit (AU) is approximately equal to 149,597,870.7 kilometers. Here is a detailed, step-by-step explanation to find the distance in AU:
1. Understand the conversion factor:
- 1 AU = 149,597,870.7 kilometers.
2. Write the relationship we need:
To convert kilometers to AU, we divide the distance in kilometers by the number of kilometers in one AU:
[tex]\[ \text{Distance in AU} = \frac{\text{Distance in km}}{\text{Kilometers per AU}} \][/tex]
3. Plug in the given values:
- Distance of the asteroid in kilometers \( = 700,000,000 \) km.
- Kilometers per AU \( = 149,597,870.7 \) km.
4. Perform the division:
[tex]\[ \text{Distance in AU} = \frac{700,000,000 \text{ km}}{149,597,870.7 \text{ km/AU}} \][/tex]
5. Calculate the result:
[tex]\[ \text{Distance in AU} \approx 4.679210985587912 \][/tex]
So, the distance of the asteroid from Earth is approximately \( 4.679 \) AU. This value is closest to 4.5 AU among the options provided.
Therefore, the distance of the asteroid from Earth is about 4.5 AU.
1. Understand the conversion factor:
- 1 AU = 149,597,870.7 kilometers.
2. Write the relationship we need:
To convert kilometers to AU, we divide the distance in kilometers by the number of kilometers in one AU:
[tex]\[ \text{Distance in AU} = \frac{\text{Distance in km}}{\text{Kilometers per AU}} \][/tex]
3. Plug in the given values:
- Distance of the asteroid in kilometers \( = 700,000,000 \) km.
- Kilometers per AU \( = 149,597,870.7 \) km.
4. Perform the division:
[tex]\[ \text{Distance in AU} = \frac{700,000,000 \text{ km}}{149,597,870.7 \text{ km/AU}} \][/tex]
5. Calculate the result:
[tex]\[ \text{Distance in AU} \approx 4.679210985587912 \][/tex]
So, the distance of the asteroid from Earth is approximately \( 4.679 \) AU. This value is closest to 4.5 AU among the options provided.
Therefore, the distance of the asteroid from Earth is about 4.5 AU.
