Accepted answer
Answer included
Problem
The keyword “4.3 8 how far away is” is interpreted as the distance \(4.3 \times 10^8\) meters (scientific notation). Convert this distance to kilometers and miles, then compare its scale to a familiar reference distance.
Assumption for comparison: mean Earth–Moon center-to-center distance \(\approx 3.84 \times 10^5\ \text{km}\).
Step 1: Read the scientific notation
The quantity \(4.3 \times 10^8\ \text{m}\) means \(4.3\) multiplied by \(10^8\) meters:
\[
4.3 \times 10^8\ \text{m} = 430{,}000{,}000\ \text{m}.
\]
Step 2: Convert meters to kilometers
Since \(1\ \text{km} = 10^3\ \text{m}\), divide by \(10^3\):
\[
4.3 \times 10^8\ \text{m}
= \frac{4.3 \times 10^8}{10^3}\ \text{km}
= 4.3 \times 10^5\ \text{km}
= 430{,}000\ \text{km}.
\]
Step 3: Convert meters to miles
Using \(1\ \text{mile} = 1609.344\ \text{m}\):
\[
\text{miles}
= \frac{4.3 \times 10^8\ \text{m}}{1609.344\ \text{m/mile}}
\approx 2.67 \times 10^5\ \text{miles}
\approx 267{,}190\ \text{miles}.
\]
Step 4: Interpret “how far away” by comparing scales
Compared to the mean Earth–Moon distance \(\approx 3.84 \times 10^5\ \text{km}\), the given distance is:
\[
\frac{430{,}000}{384{,}000} \approx 1.12,
\quad \text{so it is about } 12\% \text{ farther than the Earth–Moon distance.}
\]
| Quantity | Value | Meaning |
|---|---|---|
| Given distance | \(4.3 \times 10^8\ \text{m}\) | Scientific-notation form of a large displacement/distance |
| In kilometers | \(4.3 \times 10^5\ \text{km} = 430{,}000\ \text{km}\) | Useful for Earth–space scale comparisons |
| In miles | \(\approx 2.67 \times 10^5\ \text{miles} \approx 267{,}190\ \text{miles}\) | Common everyday unit for long distances |
| Scale comparison | \(\approx 1.12 \times\) Earth–Moon distance | “How far away” in a familiar astronomical context |
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