Question 2
Let a finite decimal fraction be given. Juku starts appending digits to this fraction in such a way that each new digit equals the remainder of the sum of all digits existing so far in division by $10$. (For instance, if the initial fraction is $27.35$ then the digits added to the end are $7$, $4$, $8$ etc.)
Prove that the infinite decimal fraction obtained this way represents a rational number.
Prove that the infinite decimal fraction obtained this way represents a rational number.