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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!

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    @Qi$a$ochu: ye$s$, I think I know how to u$s$e that one. I was hoping to get a values for n, but I guess that not possible. Thanks for your help.2011-05-24

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