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When fractions are expressed in different bases, they can be terminating or repeating.  For example, when $\frac{1}{5}$ is expressed in base $3,$ the result is
\[0.\overline{0121}_3 = 0.01210121 \dots,\]
which is repeating.

When $\frac{1}{288}$ is expressed in base $31,$ is it terminating or repeating?

 
 Jun 26, 2024

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