Repeating Decimal Multiplied to Another

Let $S_{n}$ be the result of $10^{n}-1$ , with $n$ being a positive integer. If $a$ and $b$ are positive integers and are less than $S_{n}$ , will the product be a repeating decimal when converted from fraction? $\large \frac{a}{S_{x}}×\frac{b}{S_{y}}$