I would really appreciate it if anyone could help me with this problem:
Among the convergents of $\sqrt{15}$, find a rational number that approximates $\sqrt{15}$ with accuracy to four decimal places.
I know how to find the continued fraction and the convergents for $\sqrt{15}$. But I am just not sure how to determine how far I need to go in order to approximate that number with the requested accuracy.
Thanks!