42.86% responded “Yes” on an opinion poll. How many people responded?

[Joe Horn]

The following compound fraction is an example of a "simple continued fraction":\[3+\frac { 1 }{ 7+\frac { 1 }{ 16+\frac { 1 }{ 11 } } } \]This simple continued fraction evaluates exactly to 3.1416. Converting decimal numbers and ordinary fractions into simple continued fractions and back again is essential for certain kinds of tasks, such as answering the question in this posting's title.

The attached article, presented at HHC 2012, is a step-by-step tutorial all about simple continued fractions, with many examples, and with 3 tiny User RPL routines to automate the various conversions.

TABLE OF CONTENTS:

1. How to convert decimal fractions & simple fractions into continued fractions.
   
   1. Step-by-step example.
   2. Generalized method.
   3. User RPL implementation:
      
      1. '→SF' (decimal fraction to Simple Fraction)
      2. '→CF' (simple fraction to Continued Fraction)
2. How to convert continued fractions into simple fractions & decimal fractions.
   
   1. Step-by-step example.
   2. Generalized method.
   3. User RPL implementation: 'CF→' (continued fraction to simple fraction.)
3. Fun application: 42.86% responded “Yes” on an opinion poll. How many people responded?
4. Glossary.

Attachment: ContinuedFractions.pdf (342 KB)