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

 Aug 14, 2017
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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.

 

laugh

 Aug 15, 2017
edited by heureka  Aug 15, 2017

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