Write 0.630630630... as a fraction.
Write 0.630 630 630 ... as a fraction.
Let x = 0.630 630 630 ...
then 1000x = 630.630 630 630 ...
Subtracting: 1000x = 630.630 630 630 ...
- x = 0.630 630 630 ...
999x = 630
dividing: x = 630 / 999
simplifying: x = 70/111
