Which of the following time measuring devices is most precise?

Option $(B)$ is correct because a clock can measure time correctly up to one second. A stopwatch can measure time correctly up to a fraction of a second. A digital watch can measure time up to a fraction of second whereas an atomic clock is the most accurate timekeeper and is based on characteristic frequencies of radiation emitted by certain atoms having a precision of about $1$ second in $300,000$ years. So an atomic clock can measure time most precisely as the error of this clock is about $1 s$ in $10^{13} s$.