To find the maximum distance between the Earth and Mercury, we need to subtract the distance between Mercury and the Sun from the distance between the Earth and the Sun. Here is the detailed step-by-step solution:
1. Identify Given Values:
- The maximum distance between the Sun and Mercury: [tex]\( 7 \times 10^7 \)[/tex] km
- The maximum distance between the Sun and the Earth: [tex]\( 1.5 \times 10^8 \)[/tex] km
2. Set Up the Subtraction:
The maximum distance between the Earth and Mercury is found by subtracting the distance from the Sun to Mercury from the distance from the Sun to the Earth.
[tex]\[
\text{Distance}_{\text{Earth to Mercury}} = \text{Distance}_{\text{Sun to Earth}} - \text{Distance}_{\text{Sun to Mercury}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Distance}_{\text{Earth to Mercury}} = (1.5 \times 10^8 \text{ km}) - (7 \times 10^7 \text{ km})
\][/tex]
3. Perform the Subtraction:
To subtract these two numbers, it's easiest to write them with the same exponent:
- [tex]\( 1.5 \times 10^8 = 150 \times 10^6 \)[/tex]
- [tex]\( 7.0 \times 10^7 = 70 \times 10^6 \)[/tex]
Then subtract:
[tex]\[
(150 \times 10^6) - (70 \times 10^6) = (150 - 70) \times 10^6 = 80 \times 10^6
\][/tex]
Therefore,
[tex]\[
80 \times 10^6 \text{ km}
\][/tex]
4. Express the Answer in Scientific Notation:
Write [tex]\( 80 \times 10^6 \)[/tex] in standard scientific notation:
[tex]\[
80 \times 10^6 = 8.0 \times 10^7 \text{ km}
\][/tex]
Thus, the maximum distance between the Earth and Mercury is [tex]\( 8.0 \times 10^7 \)[/tex] kilometers.
