Here's a version based on the answer at http://stackoverflow.com/questions/12098461/how-can-i-detect-if-a-float-has-a-repeating-decimal-expansion-in-c/12101996#12101996
It's hard coded to look for an approximation to 1.2734, and 10 iterations - its output is :
0 1/1 = 1.000000 (eps = -0.273400)
1 4/3 = 1.333333 (eps = 0.059933)
2 5/4 = 1.250000 (eps = -0.023400)
3 9/7 = 1.285714 (eps = 0.012314)
4 14/11 = 1.272727 (eps = -0.000673)