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Choice C is correct. It's given that during an assembly, students occupied $50\%$ of the $840$ seats in the school auditorium. Therefore, the number of seats that the students occupied during this assembly can be calculated by multiplying the number of seats in the school auditorium by $\frac{50}{100}$. Thus, the students occupied $840\left(\frac{50}{100}\right)$, or $420$, seats during this assembly.

Choice A is incorrect. This is approximately $3\%$, not $50\%$, of $840$.

Choice B is incorrect. This is approximately $6\%$, not $50\%$, of $840$.

Choice D is incorrect. This is approximately $94\%$, not $50\%$, of $840$.