An infinite decimal expansion means there is no end to the 9s.
Let x = 0.999999........ to infinity
Then 10x = 9.999999....... also to infinity
Subtract x from 10x. The infinite number of 9s to the right of the decimal points cancel and we have:
9x = 9
Hence x = 1. i.e. 1 = 0.99999............ to infinity