Imagine a timing system set-up where you have a pendulum that swings from a fixed release point, through the start, then shortly after through the finish. You release this pendulum 1000 times through the timing system. Since it is released from the same point exactly the same way every time, you would expect the times to be identical for all 1000 "races" , right? If your timing system displays in seconds, they will all be the same (most likely). If the timing system displays in .1 second, or .01 second, they display all the same values. Somewhere after adding enough digits, you will not be displaying differences in the "race" (because all races are identical), but displaying differences in the random errors inherent in the timing system. (perhaps at .0001 second, perhaps at .001 ???)
In actual practice, you may not be able to tell if the pendulum is ACTUALLY going minutely slower or faster, or if the timing system is displaying slower or faster.