x = 0.(13)
100x = 13.(13)
100x - x = 13.(13) - 0.(13)
99x = 13
x = 13/99
x = 0.2(17)
10x = 2.(17)
1000x = 217.(17)
1000x - 10x = 217.(17) - 2.(17)
990x = 215
x =215/990 = 43/198
x = 0.(13)
100x = 13.(13)
100x - x = 13.(13) - 0.(13)
99x = 13
x = 13/99
x = 0.2(17)
10x = 2.(17)
1000x = 217.(17)
1000x - 10x = 217.(17) - 2.(17)
990x = 215
x =215/990 = 43/198