Solutions to Problems 1481 - 1490

Q1481 Prove that if the denominator $q$ of a fraction $p/q$ is the number consisting of $n$ digits, all equal to $9$, and if $p$ is less than $q$, then $p/q$ can be written as a repeating decimal in which the repeating part has length $n$ and contains the digits of $p$, preceded by a sufficient number of $0$s to give that length.