Decimals Into Fractions Part II

In a previous article "Decimals Into Fractions" in Consortium 92, Spring/Summer 2007, we developed and proved an algorithm for finding the smallest denominator D so that a decimal number x can be written as x = to a prescribed degree of accuracy. (We called the sequence of approximations a "Farey Series.")We used the example x = 0.579 accurate to three decimal places, and found that the rational number with smallest denominator to produce this answer is . Table 1 is a tabular form of the algorithm.