1/98 = 0.01 02 04 08 16 32 ...
1/998 = 0.001 002 004 008 016 032 064 128 256 ...
but there's also a degenerate case, where you have no 9s at all:
1/8 = 0.1 + 0.02 + 0.004 + 0.0008 + ...
and what's surprising here is that everything adds up and gives you the terminating decimal 0.125 that you were expecting.
The sum of a convergent series is a / (1 - r) where a is the first value, and r is the ratio between the n+1th and nth term.
a = 1/10, r = 1/5 n = (1 / 10) / (1 - (1 / 5)) n = (1 / 10) / (4 / 5) n = 5 / 40 n = 1 / 8
1/98 = 0.01 02 04 08 16 32 ...
1/998 = 0.001 002 004 008 016 032 064 128 256 ...
but there's also a degenerate case, where you have no 9s at all:
1/8 = 0.1 + 0.02 + 0.004 + 0.0008 + ...
and what's surprising here is that everything adds up and gives you the terminating decimal 0.125 that you were expecting.