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The problem requires us to convert a distance of [tex]\(27.7 \times 10^{11}\)[/tex] meters into multiple other units: gigameters, terameters, petameters, and megameters. Here is the step-by-step solution to convert the distance into each of these units:
### 1. Converting to Gigameters
A gigameter (Gm) is equal to [tex]\(10^9\)[/tex] meters.
[tex]\[ \text{Distance in gigameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^9 \, \text{m/Gm}} \][/tex]
[tex]\[ \text{Distance in gigameters} = \frac{27.7 \times 10^{11}}{10^9} \][/tex]
[tex]\[ \text{Distance in gigameters} = 27.7 \times 10^2 \][/tex]
[tex]\[ \text{Distance in gigameters} = 2770.0 \, \text{Gm} \][/tex]
### 2. Converting to Terameters
A terameter (Tm) is equal to [tex]\(10^{12}\)[/tex] meters.
[tex]\[ \text{Distance in terameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^{12} \, \text{m/Tm}} \][/tex]
[tex]\[ \text{Distance in terameters} = \frac{27.7 \times 10^{11}}{10^{12}} \][/tex]
[tex]\[ \text{Distance in terameters} = 2.77 \times 10^{-1} \][/tex]
[tex]\[ \text{Distance in terameters} = 2.77 \, \text{Tm} \][/tex]
### 3. Converting to Petameters
A petameter (Pm) is equal to [tex]\(10^{15}\)[/tex] meters.
[tex]\[ \text{Distance in petameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^{15} \, \text{m/Pm}} \][/tex]
[tex]\[ \text{Distance in petameters} = \frac{27.7 \times 10^{11}}{10^{15}} \][/tex]
[tex]\[ \text{Distance in petameters} = 2.77 \times 10^{-4} \][/tex]
[tex]\[ \text{Distance in petameters} = 0.00277 \, \text{Pm} \][/tex]
### 4. Converting to Megameters
A megameter (Mm) is equal to [tex]\(10^6\)[/tex] meters.
[tex]\[ \text{Distance in megameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^6 \, \text{m/Mm}} \][/tex]
[tex]\[ \text{Distance in megameters} = \frac{27.7 \times 10^{11}}{10^6} \][/tex]
[tex]\[ \text{Distance in megameters} = 27.7 \times 10^5 \][/tex]
[tex]\[ \text{Distance in megameters} = 2770000.0 \, \text{Mm} \][/tex]
### Final Results
- Distance in gigameters: [tex]\(2770.0\)[/tex] Gm
- Distance in terameters: [tex]\(2.77\)[/tex] Tm
- Distance in petameters: [tex]\(0.00277\)[/tex] Pm
- Distance in megameters: [tex]\(2770000.0\)[/tex] Mm
These results represent the converted distances from meters into gigameters, terameters, petameters, and megameters.
### 1. Converting to Gigameters
A gigameter (Gm) is equal to [tex]\(10^9\)[/tex] meters.
[tex]\[ \text{Distance in gigameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^9 \, \text{m/Gm}} \][/tex]
[tex]\[ \text{Distance in gigameters} = \frac{27.7 \times 10^{11}}{10^9} \][/tex]
[tex]\[ \text{Distance in gigameters} = 27.7 \times 10^2 \][/tex]
[tex]\[ \text{Distance in gigameters} = 2770.0 \, \text{Gm} \][/tex]
### 2. Converting to Terameters
A terameter (Tm) is equal to [tex]\(10^{12}\)[/tex] meters.
[tex]\[ \text{Distance in terameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^{12} \, \text{m/Tm}} \][/tex]
[tex]\[ \text{Distance in terameters} = \frac{27.7 \times 10^{11}}{10^{12}} \][/tex]
[tex]\[ \text{Distance in terameters} = 2.77 \times 10^{-1} \][/tex]
[tex]\[ \text{Distance in terameters} = 2.77 \, \text{Tm} \][/tex]
### 3. Converting to Petameters
A petameter (Pm) is equal to [tex]\(10^{15}\)[/tex] meters.
[tex]\[ \text{Distance in petameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^{15} \, \text{m/Pm}} \][/tex]
[tex]\[ \text{Distance in petameters} = \frac{27.7 \times 10^{11}}{10^{15}} \][/tex]
[tex]\[ \text{Distance in petameters} = 2.77 \times 10^{-4} \][/tex]
[tex]\[ \text{Distance in petameters} = 0.00277 \, \text{Pm} \][/tex]
### 4. Converting to Megameters
A megameter (Mm) is equal to [tex]\(10^6\)[/tex] meters.
[tex]\[ \text{Distance in megameters} = \frac{27.7 \times 10^{11} \, \text{m}}{10^6 \, \text{m/Mm}} \][/tex]
[tex]\[ \text{Distance in megameters} = \frac{27.7 \times 10^{11}}{10^6} \][/tex]
[tex]\[ \text{Distance in megameters} = 27.7 \times 10^5 \][/tex]
[tex]\[ \text{Distance in megameters} = 2770000.0 \, \text{Mm} \][/tex]
### Final Results
- Distance in gigameters: [tex]\(2770.0\)[/tex] Gm
- Distance in terameters: [tex]\(2.77\)[/tex] Tm
- Distance in petameters: [tex]\(0.00277\)[/tex] Pm
- Distance in megameters: [tex]\(2770000.0\)[/tex] Mm
These results represent the converted distances from meters into gigameters, terameters, petameters, and megameters.
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