Fun fact : 3.125 is the new reward after the halving, expressed as sats, dropping trailing zeros:
3125 = 5*5*5*5*5
Little quiz: is this always true (power of 5) for every reward value?
Discussion
3.125 is the subsidy, not the reward
Here's an answer, any corrections welcome:
in sats, the original subsidy is 5 billion = 5*10^9 = 5^10*2^9
That means that after 9 halvings we have a pure power of 5 number of sats. So after the 10th halving that's no longer true and rounding has to happen.
After 9th halving: 9765625 sats (=5^10).
After 10th, 4882812.5 (no longer whole number so pattern breaks).
I believe it always rounds down, but the internal calculation, for the next halving, includes the full number, meaning the pattern 'internally' continues all the way to the end (think of a decimal number as an infinite sequence of powers of 10)