Not to discourage you, but you really need a more efficient algorithm. Your algorithm is O^2 at best, and as the need for accuracy increases, the performance penalty gets greater and greater.

Here's an alternative very fast and efficient log(log(O)) algorithm: A fraction can be expressed as the sum (or difference) of a series of fractions:
0.35 = 1/28 - 1/6 - 1/60 = 7/20
0.35 = int (1/0.35) - int (1/(1 - int(1/0.35))) ...

[download]

Which is a perfect candidate for a recursive function. I implement the following demo to show how this can be done. Hopefully you might find it useful. :-) 
use strict;
use warnings;

while (<DATA>) {
    chomp;

    my ($den, $div, $error) = fraction($_);

    print "$_\t$den/$div\n";
}

sub fraction
{
    my $value = shift;

    my $a = 1;
    my $b = int(1 / $value);
    my $c = (1 / $b) - $value;  # error

    return ($a, $b, $c) if $c < 0.0005;

    my ($d, $e, $f) = fraction($c);

    my $g = $a * $e - $d * $b;
    my $h = $b * $e;
    
    for (2,3,5,7) { # reduces 2/4 => 1/2, 3/27 => 1/9, etc.
        ($g, $h) = reduce($g, $h, $_);
    }

    return ($g,
            $h,
            $f);
}

sub reduce
{
    my ($a, $b, $base) = @_;
    while ($a % $base == 0 && $b % $base == 0) {
        $a = $a / $base;
        $b = $b / $base;
    }
    return ($a, $b);
}



__DATA__
0.035
0.037
0.039
0.041
0.043
0.046
0.048
0.058
0.068
0.078
0.35
0.37
0.39
0.41
0.43
0.46
0.48
0.58
0.68
0.78

[download]

And the output -
0.035   7/200
0.037   1/27
0.039   974/24975
0.041   41/1000
0.043   1/23
0.046   596/12957
0.048   479/9980
0.058   1197/20638
0.068   277/4074
0.078   175/2244
0.35    7/20
0.37    57/154
0.39    6311/16182
0.41    4961/12100
0.43    43/100
0.46    23/50
0.48    47/98
0.58    2081/3588
0.68    151/222
0.78    103/132

[download]

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

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