1. At first the difficult part for me was understanding the initial example of approximating pi using continued fractions, but after a second reading and closer examination, it came just fine. However, there is still this part toward the end of the section where they approximate 12345/11111 using continued fractions. They have a list of fractions they get after applying the same procedure. I'm not sure exactly how they get that list. I'm assuming that they get it by doing 1, 1+1/9, 1+1/(9+1/246), etc.
2. My remaining questions is, is there a quick way to do this backward? That is, if we are given a continued fraction is there a quick way of determining what rational number the continued fractions represent without having to use a calculator and arduously type the continued fraction in?
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