How do you turn recurring decimals into fractions?
-- Take one whole set of the digits that repeat in the decimal.
Write them as the numerator of the fraction.
-- For the denominator of the fraction, write a group of 9s ... the same
number of them as there are digits in the numerator.
-- Simplify the fraction, if possible and if you feel like it.
All rational fractions - one integer divided by a non-zero integer - give rise to repeating or terminating decimals. If, for the fraction in its simplest form, the denominator can be expressed as a product of powers of only 2 and 5 then the decimal will terminate. If the denominator has any prime factor other than 2 or 5 the decimal will be recurring. All non-rational fractions will have infinite, non-recurring decimal representations.