Question 1207598
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The fraction 1/n, when expressed in base b, will terminate if and only if the prime factorization of n contains only factors that are prime factors of the base b.<br>
For example, in our familiar base 10 system, since the prime factorization of 10 is 2*5, a fraction 1/n will terminate if and only if the prime factorization of n contains only 2's and 5's.<br>
In your example, the base 13 is a prime number, so 1/n expressed in base 13 will terminate if and only if the prime factorization of n contains only 13's -- i.e., if and only if n is a power of 13.<br>
288 is not a power of 13, so 1/288 expressed in base 13 will not terminate.<br>
ANSWER: Repeating<br>