Number Theory

First, let's convert 1/288 into base 25 form. 

We get that $(BD)_{25} = (11 × 25^1) + (13 × 25^0) = (288)_{10}$

This means that $\frac{1}{288}_{10} = \frac{1}{BD}_{25}$

Doing base division, we have that

$\frac{1}{BD}_{25} = 0.\overline{0.02468ACEGIKN}$

So when $\frac{1}{288}$ is in base 25, the decimal is repeating. 

So repeating is our answer. 

Thanks! :)