\(What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 9?\)
What is the smallest positive integer \(n\) such that \( \tfrac{1}{n}\)
is a terminating decimal and \(n \) contains the digit \(9\) ?
Terminating decimal if and only n (denominator) is of the form \(2^r5^s\)
The smallest positive integer \(n\):
\(\begin{array}{|rcll|} \hline 2^{12}\cdot 5^0 &=& 4096 \\ && \frac{1}{4096} = 0.000244140625 \\ \hline \end{array}\)
The smallest positive integer n is 4096.