Answer :
To calculate the number of astronomical units between Mercury and Jupiter, given the distance in kilometers, we'll follow these steps:
Step 1: Understand the units involved:
- The astronomical unit (AU) is a standard unit of distance in astronomy, which is approximately equal to the average distance between the Earth and the Sun.
- The distance in kilometers (km) is a measurement of length in the metric system.
Step 2: Define the problem's given values:
- The distance between Mercury and Jupiter is given as \(7.2 \times 10^8\) kilometers.
Step 3: Define the value of one astronomical unit in kilometers:
- One astronomical unit (AU) is equal to 149,597,870.7 kilometers.
Step 4: Use the given values to calculate the distance in astronomical units:
- Distance in astronomical units (AU) can be found by dividing the distance in kilometers by the length of one astronomical unit:
\[ \text{Distance in AU} = \frac{\text{Distance between Mercury and Jupiter in km}}{\text{Length of one AU in km}} \]
Step 5: Plug in the given values and calculate:
\[ \text{Distance in AU} = \frac{7.2 \times 10^8 \text{ km}}{149,597,870.7 \text{ km/AU}} \]
Step 6: Calculate the division to find the answer:
- Perform the division using the given numbers to find the number of astronomical units between Mercury and Jupiter.
\[ \text{Distance in AU} \approx \frac{7.2 \times 10^8}{149,597,870.7} \]
\[ \text{Distance in AU} \approx 4.814 \]
Step 7: State the final answer:
- The distance between Mercury and Jupiter is approximately 4.814 astronomical units.
