It is claimed that two cesium clocks,if allowed to run for $100$ years,free from any disturbance,may differ by only about $0.02\; s$. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of $1\; s$?

(N/A) The total time duration is $100$ years.
Converting this into seconds: $100 \times 365 \times 24 \times 60 \times 60 = 3.15 \times 10^{9} \; s$.
The total time difference between the two clocks over this duration is $0.02 \; s$.
To find the accuracy for a $1 \; s$ interval,we calculate the relative error or the precision per unit time.
The error per unit time is $\frac{0.02 \; s}{3.15 \times 10^{9} \; s} \approx 6.35 \times 10^{-12} \; s$.
This means that for every $1 \; s$ measured,the clock is accurate to within approximately $6 \times 10^{-12} \; s$.