Difference in time of caesium clocks = 0.02 s
Time required for this difference = 100 years
= 100 × 365 × 24 × 60 × 60 = 3.15 × 109 s
In 3.15 × 109 s, the caesium clock shows a time difference of 0.02 s
In 1s, the clock will show a time difference of (0.02/3.15 x 109)s
Hence, the accuracy of a standard caesium clock in measuring a time interval of 1 s is
3.15 x 109/0.02 = 157.5 x 109 s ≈ 1.5 x 1011 s