x is an integer such that ‎1≤x≤9, Prove that 0.(0x)recurring=x/99

r=0.0^.x^.

^{r=0.0x0x0x0x....}

^{100r=x.0x0x0x     (1)}

^{10,000r=x0x.0x0x0x      (2)}

^{(2) - (1):  9,900r=x00}

^{r=x00/9,990        r=x/99}