Did you look at the link provided to Continued Fractions?

Sure, the approach there is more complex, but the method provided does a better job of producing a rapidly converging sequence of fractional approximations than yours does. Modifying it to stop when the next approximation is more than 100, I produce the following output on your dataset: 

2/57  =  0.0350877192982456
1/27  =  0.037037037037037
3/77  =  0.038961038961039
3/73  =  0.0410958904109589
4/93  =  0.043010752688172
4/87  =  0.0459770114942529
1/21  =  0.0476190476190476
4/69  =  0.0579710144927536
3/44  =  0.0681818181818182
6/77  =  0.0779220779220779
7/20  =  0.35
37/100  =  0.37
39/100  =  0.39
41/100  =  0.41
43/100  =  0.43
23/50  =  0.46
12/25  =  0.48
29/50  =  0.58
17/25  =  0.68
39/50  =  0.78

[download]
For half of them it found the actual fraction. For the other half it was never off by more than 0.0001. If you let it go to a denominator of 1000, it correctly identified every fraction, and put it in lowest terms.

(There are other tricks that I used there, like a GCD algorithm that is completely general and more efficient than trial division.)

In reply to Re: Re: Percentages to Fractions by tilly
in thread Percentages to Fractions by David Caughell

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