The maximum distance between the Sun and Mercury is [tex]$7 \times 10^7 \text{ km}$[/tex], while the maximum distance between the Sun and the Earth is [tex]$1.5 \times 10^8 \text{ km}$[/tex]. What is the maximum distance between the Earth and Mercury in kilometers? Express your answer in scientific notation.

[tex]\boxed{} \times 10 \text{ km}[/tex]



Answer :

To find the maximum distance between the Earth and Mercury, given their maximum distances from the Sun, we can follow these steps:

1. Identify the given distances:
- The maximum distance between the Sun and Mercury is [tex]\( 7 \times 10^7 \text{ km} \)[/tex].
- The maximum distance between the Sun and the Earth is [tex]\( 1.5 \times 10^8 \text{ km} \)[/tex].

2. Calculate the maximum distance between the Earth and Mercury:
- We need to find the difference between the maximum distance of the Earth from the Sun and the maximum distance of Mercury from the Sun.
- This difference is:
[tex]\[ 1.5 \times 10^8 \text{ km} - 7 \times 10^7 \text{ km} \][/tex]
- Converting these into the same power of ten, we get:
[tex]\[ 1.5 \times 10^8 \text{ km} = 1.5 \times 10^8 \text{ km} \][/tex]
[tex]\[ 7 \times 10^7 \text{ km} = 0.7 \times 10^8 \text{ km} \][/tex]
- Subtract the two distances:
[tex]\[ 1.5 \times 10^8 \text{ km} - 0.7 \times 10^8 \text{ km} = 0.8 \times 10^8 \text{ km} \][/tex]

3. Express the result in scientific notation:
- The distance [tex]\( 0.8 \times 10^8 \text{ km} \)[/tex] can be expressed as:
[tex]\[ 8.0 \times 10^7 \text{ km} \][/tex]

Therefore, the maximum distance between the Earth and Mercury is:

[tex]\[ \boxed{8.0} \times 10^7 \text{ kilometers} \][/tex]