Let x=0.166666...-----------(1equation)
Multiplying by 10 in both sides
10x=1.66666...-------------(2equation)
Multiplying by 10 in both sides
100x=16.6666...----------(3equation)
Subtracting 2equation from 3equation
100x-10x=16.666..-1.666..
90x=15
x=15/90
0.16666....=15/90
