Let's say I have a stopwatch that can take split times. It's resolution is 1/100th of a second. Let's also say I have a robot that can press the split button exactly 0.244s apart in real time. I have the robot take 3 splits.
What should the splits on the stopwatch show and what would be the final time?
0.244 real time can only be displayed as 0.24 or 0.25 on the stopwatch due to the 1/100th second resolution, right? But then, 0.24 x 3 = 0.72 and 0.25 x 3 = 0.75; the real time that has elapsed is 0.732...
The main clock is running all the time so when the robot presses for the first split 0.244 seconds have elapsed and the stopwatch displays 0.24. The clock is still running, it has not stopped and been restarted so when the robot presses for the second split the elapsed time is 0.488 seconds so the clock displays 0.48 when the robot presses for the third split 0.732 seconds have elapsed and the clock displays 0.73.
The point to remember here is that pressing the 'split' button just freezes the display the timer is still running in the background.
Alternatively on a stop watch that was displaying the incremental times only such as lap times I'd expect it to simply subtract the old split time from the current time.
So I would expect this to show $0.24$ then $0.48 - 0.24 = 0.24$ and finally $0.73 - 0.48 = 0.25$ All split times being simply the time now minus the time at the previous split.