It is well known that every decimal of a fraction becomes periodic at one point or the other, e.g: 1/3 starts repeating at period 1, 27/91 at period 6 and 3923/6173 at period 3086.
Now, as there are an infinite number of non-zero values that we may place in the numerator or denominator of a fraction, the following question arises: does there exist a fraction whose repeating decimal has a period of some highest number or can the number of this period take infinitely many values?
In other words, does there exist some fraction whose repeating decimal has a period of 577291485 or even 5*10^444? And furthermore, is it true that there are an infinite number of fractions whose decimal number has the period 5?
It should be kept in mind however that the numerator/denominator of the fractions in question may contain numbers not repeating thrice/twice, e.g: 586192/247591, or 1/43817 and 1/39820, so it's not just 1/9 or 1/999.