Any decimal that repeats can be expressed a a rational number with integer numerator and denominator...
This is the procedure to finding the rational fraction
x=0.111..... then you multiply this x so that it is greater than 1 but still has the same repeating decimal portion, here we just need to multiply by 10 so:
10x=1.111....
Now you subtract the repeating decimal from the multiple of x...
10x=1.111...
- x=0.111...
9x=1 now just get x by itself..
x=1/9
This procedure works for any repeating decimal...
