Convert a decimal number to a fraction / rational number

Question

In JavaScript, is there any way to convert a decimal number (such as 0.0002) to a fraction represented as a string (such as \"2/10000\")?

I

Answer 1

I used this site http://mathforum.org/library/drmath/view/51886.html to build a function but as the article mentions you will get an unreasonable large number for radicals or pi.

Hope it helps though.

function Fraction(){}
Fraction.prototype.convert = function(x, improper)
{
    improper = improper || false;
    var abs = Math.abs(x);
    this.sign = x/abs;
    x = abs;
    var stack = 0;
    this.whole = !improper ? Math.floor(x) : 0;
    var fractional = !improper ? x-this.whole : abs;
    /*recursive function that transforms the fraction*/
    function recurs(x){
        stack++;
        var intgr = Math.floor(x); //get the integer part of the number
        var dec = (x - intgr); //get the decimal part of the number
        if(dec < 0.0019 || stack > 20) return [intgr,1]; //return the last integer you divided by
        var num = recurs(1/dec); //call the function again with the inverted decimal part
        return[intgr*num[0]+num[1],num[0]]
    }
    var t = recurs(fractional); 
    this.numerator = t[0];
    this.denominator = t[1];
}

Fraction.prototype.toString = function()
{
    var l  = this.sign.toString().length;
    var sign = l === 2 ? '-' : '';
    var whole = this.whole !== 0 ? this.sign*this.whole+' ': sign;
    return whole+this.numerator+'/'+this.denominator;
}

//var frac = new Fraction()
//frac.convert(2.56, false)
//console.log(frac.toString())
//use frac.convert(2.56,true) to get it as an improper fraction

If you just want a self-contained function that only returns the numerator and denominator then use the function below.

var toFraction = function (dec) {
    var is_neg = dec < 0;
    dec = Math.abs(dec);
    var done = false;
    //you can adjust the epsilon to a larger number if you don't need very high precision
    var n1 = 0, d1 = 1, n2 = 1, d2 = 0, n = 0, q = dec, epsilon = 1e-13;
    while (!done) {
        n++;
        if (n > 10000) {
            done = true;
        }
        var a = parseInt(q);
        var num = n1 + a * n2;
        var den = d1 + a * d2;
        var e = (q - a);
        if (e < epsilon) {
            done = true;
        }
        q = 1 / e;
        n1 = n2;
        d1 = d2;
        n2 = num;
        d2 = den;
        if (Math.abs(num / den - dec) < epsilon || n > 30) {
            done = true;
        }
    }
    return [is_neg ? -num : num, den];
};
//Usage:
//var frac = toFraction(0.5);
//console.log(frac)
//Output: [ 1, 2 ]