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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?

 
 Oct 23, 2024

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