A JavaScript function to find short rational number representations of floating point numbers, with the help of some continued fractions.

float2rat.js

    // See http://jonisalonen.com/2012/converting-decimal-numbers-to-ratios/
    // Also https://en.wikipedia.org/wiki/Diophantine_approximation
    // or french https://fr.wikipedia.org/wiki/Fraction_continue_et_approximation_diophantienne

    function float2rat(x) {

        var tolerance = 1.0E-6;
        var max_iter = 100; // Limit on the amount of work we want to do
        var max_den = 1000; // When is a fraction not really more helpfull than decimal ?

        //Integer
        if( Math.abs(x - Math.round(x)) < tolerance )
            return ""+Math.round(x);

        // Store the sign and continue as positive number
        var sgn = x>=0?1:-1;
        x = Math.abs(x);
        var b = x;

        // Prepare continued fractions expansion
        var h1=1; var h2=0;
        var k1=0; var k2=1;

        for(var i=0;i<max_iter;i++){

            var a = Math.floor(b);
            var tmp;

            tmp = h1;
            h1 = a*h1+h2;
            h2 = tmp;

            tmp = k1;
            k1 = a*k1+k2;
            k2 = tmp;

            b = 1/(b-a);

            // Success
            if( Math.abs(k1*x-h1) <=  k1*tolerance){
                return sgn*h1+"/"+k1;
            }
            
            // Reached max denominator, nothing of interest, goto failure.
            if(k1 >= max_den ){
                break;
            }
            
        }

        // Failure to find small fraction, present a decimal
        return x.toFixed(6)

    }