order of magnitude

Question

Earth's radius ≈ 6.37×10^6 m. Its order of magnitude is:

RankGuru · Accepted Answer

To find the order of magnitude of a number $x \cdot 10^n$:
- If $x \leq \sqrt{10} \approx 3.16$, the order of magnitude is $10^n$.
- If $x > \sqrt{10} \approx 3.16$, the order of magnitude is $10^{n+1}$.
Here, $x = 6.37$, which is greater than $3.16$. Therefore, the order of magnitude is $10^{6+1} = 10^7 	ext{ m}$.

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