\(What is the smallest positive integer $n$ such that $\frac{1}{n}$ is a terminating decimal and $n$ contains the digit 9?\)

Guest Aug 14, 2017

#1**+1 **

**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**.

heureka
Aug 15, 2017