x = 0.352171717
This is a repeating decimal:
Take it apart
0.352 + 0.000171717 = 0.352171717
as e^(i*pi) showed in his post:
= 0.352171717
you can see that 352/1000 can be reduced
so add the fractions
need a common denominator
and that can be reduced:
divide numerator & denominator by 625 to get the fraction in lowest terms.
Spoiler:
The continued fraction algorithm is the method of choice for doing this type of conversions.
The above is not that algorithm.
Perhaps someone will explain/demonstrate the continued fraction algorithm for converting decimals to rationals.