Prove that any number, with zeros standing in all decimal places numbered $10^n$ and only in these places, is irrational

Question

Prove that any number, with zeros standing in all decimal places numbered $10^n$ and only in these places, is irrational.

This question I got from the book Problems in Calculus of One Variable by I.A.Maron. I can't get what the question means even. Any insight will be helpful

Answer 1

Rational numbers have eventually periodic decimal expansions. Suppose the period is of length $d$, the periodic sequence starts on place $q$ and $10^n>q$. Then the digit on place $10^n+kd$ for every positive integer $k\ge 1$ must be 0. So $ 10^n+kd$ should be a power of $10$ for every $k$, a contradiction.