[coldcache]

To add on to this, the question then can become why can’t the number start repeating after a certain point (e.g., 3.14133333333…). But then we can represent it as a sum of 3.141 and 0.000333333…, i.e., two rational numbers. Then we can construct a fraction that represents the number.

[empath75]

and it can also be shown that all rational numbers repeat because there's only so many remainders possible for a given denominator (all the numbers from 0 to n-1), and as soon as you repeat a remainder, you necessarily have to repeat everything from the last occurrence of that remainder.