Question 1207598
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If in the fraction   {{{p/q}}}  the denominator is relatively prime to the base  b,

then this fraction  {{{p/q}}}  in base  b  is repeating.


This general rule is  ALWAYS  valid.



Apply it in your case.   The fraction   {{{1/288}}}   has the denominator  288  relatively prime to the base  13.


THEREFORE,  the given fraction in the given base is repeating.



Solved,  answered and explained.