8,(16) = 8 + 0.16 + 0.0016 + 0.000016 + ... = 8 + 0.16(1 + 0.01 + 0.0001 + ...) = 8 + 0.16 (1/(1-0.01)) = 8 + 0.16 (1/0.99) = 8 + 0.16 (100/99) = 8 + 1.6 (10/99) = 8 + 16/99

Поэтому 8,(16) = 8 + 16/99 = 8 99/99 + 16/99 = (8 99 + 16) / 99 = 808/99.

Итак, 8,(16) = 808/99.