What is 0.116 with the 16 repeating as an fraction?

Let y = 0.1161616…..
Then, 100y =11.6161616……

100y - y = (11.6161616……) - (0.1161616…..)
99y = 11.5
198y = 23
y = 23/198

Hence, 0.1161616…… = 23/198

Let P = 0.116161616...
Hence 1000P = 116.16161616...
& 10P = 1.1616161...
Subtract
1000P = 116.1616161....
10P = 1.16161616...
Subtract
990P = 115
P = 115/990
Cancel down by '5'
23/198

Hence 0.116161616.... = 23/198
P = 0.11616161616
999P =

0.1161616...
= 1.6161616... - 1.5
= 1 + 61/99 - 3/2
= (198 + 122 - 297)/198
= 23/198

0.1 + 0.016161616...
= 1/10 + (1/10) X (16/99)
= 1/10 + 16/990
= (99 + 16)/990
= 115/990
= 23/198