How to Find Convergents of a Continued Fraction?

[shelford]

Hi, I think I have the first part of the question correct but can't seem to get the second so any help would be fantastic.

Q: Express \frac{327}{117} as a continued fraction and find the convergents of it.

My working:
\frac{327}{117}=2 +\frac{93}{117} =2+\frac{1}{\frac{117}{93}}

\frac{117}{93}=1 + \frac{24}{93} =1+\frac{1}{\frac{93}{24}}

I continue like this to finally get:

\frac{327}{117}=2 + \frac{1}{1+ \frac{1}{3+\frac{1}{1+\frac{1}{7}}}}.

I think it is right, but I can't get the second part at all.

Thanks for any help.

 

[Xitami]

2.0000000000000 = 2
3.0000000000000 = 3
2.7500000000000 = 11/4
2.8000000000000 = 14/5
2.7948717948718 = 109/39 = 327/117