0.(7) = x
10x = 7.(7)
10x - x = 7.(7) - 0.(7)
9x = 7
x = 7/9
x = 2.4(3)
10x = 24.(3)
100x = 243.(3)
100x - 10x = 243.(3) - 24.(3)
90x = 219
x = 219/90 = 73/30
0.(7) = x
10x = 7.(7)
10x - x = 7.(7) - 0.(7)
9x = 7
x = 7/9
x = 2.4(3)
10x = 24.(3)
100x = 243.(3)
100x - 10x = 243.(3) - 24.(3)
90x = 219
x = 219/90 = 73/30