Meaning of order of magnitude

Any physical quantity can be written in scientific notation as $N = a \times 10^b$ where $1 \le a < 10$ and $b$ is an integer.

The order of magnitude is the nearest power of $10$ to the number.

Rule for deciding the order of magnitude

We compare the coefficient $a$ with $\sqrt{10} \approx 3.16$.

• If $1 \le a < 5$ (rough school/JEE convention), the order of magnitude is taken as $10^b$.
• If $5 \le a < 10$, the order of magnitude is taken as $10^{b+1}$.

Thus, in common JEE convention, $b$ is the order of magnitude exponent when $a \le 5$.

Check each option

Option A: $a$ is order of magnitude for $b \le 5$
This is incorrect. Order of magnitude is associated with a power of $10$, not with the coefficient $a$.

Option B: $b$ is order of magnitude for $a \le 5$
This is correct under the standard JEE convention.

Option C: $b$ is order of magnitude for $a \ge 5$
Incorrect. For $a \ge 5$, order of magnitude shifts to $10^{b+1}$, so exponent is not simply $b$.

Option D: $b$ is order of magnitude for $5 < a \le 10$
Incorrect for the same reason as above.

Final answer

The correct option is: $\boxed{\text{B}}$

Comparison with stored answer

Stored correct answer = B
Derived answer = B
So they agree.