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")?

If a function called decimalToFraction had been written for this purpose, then decimalToFraction(0.0002) would return the string "2/10000".

Answer 1

You can use Erik Garrison's fraction.js library to do that and more fractional operations.

var f = new Fraction(2, 10000);
console.log(f.numerator + '/' + f.denominator);

---

To to do .003 you can just do

var f = new Fraction(.003);
console.log(f.numerator + '/' + f.denominator);

Answer 2

A little googling with the term "decimal to fraction js" the first yielded this:

http://wildreason.com/wildreason-blog/2010/javascript-convert-a-decimal-into-a-simplified-fraction/

It seems to work:

http://jsfiddle.net/VKfHH/

function HCF(u, v) { 
    var U = u, V = v
    while (true) {
        if (!(U%=V)) return V
        if (!(V%=U)) return U 
    } 
}
//convert a decimal into a fraction
function fraction(decimal){

    if(!decimal){
        decimal=this;
    }
    whole = String(decimal).split('.')[0];
    decimal = parseFloat("."+String(decimal).split('.')[1]);
    num = "1";
    for(z=0; z<String(decimal).length-2; z++){
        num += "0";
    }
    decimal = decimal*num;
    num = parseInt(num);
    for(z=2; z<decimal+1; z++){
        if(decimal%z==0 && num%z==0){
            decimal = decimal/z;
            num = num/z;
            z=2;
        }
    }
    //if format of fraction is xx/xxx
    if (decimal.toString().length == 2 && 
            num.toString().length == 3) {
                //reduce by removing trailing 0's
        decimal = Math.round(Math.round(decimal)/10);
        num = Math.round(Math.round(num)/10);
    }
    //if format of fraction is xx/xx
    else if (decimal.toString().length == 2 && 
            num.toString().length == 2) {
        decimal = Math.round(decimal/10);
        num = Math.round(num/10);
    }
    //get highest common factor to simplify
    var t = HCF(decimal, num);

    //return the fraction after simplifying it
    return ((whole==0)?"" : whole+" ")+decimal/t+"/"+num/t;
}

// Test it
alert(fraction(0.0002)); // "1/5000"

Answer 3

Very old question but maybe someone can find this useful. It's iterative, not recursive and doesn't require factorization

function getClosestFraction(value, tol) {
    var original_value = value;
    var iteration = 0;
    var denominator=1, last_d = 0, numerator;
    while (iteration < 20) {
        value = 1 / (value - Math.floor(value))
        var _d = denominator;
        denominator = Math.floor(denominator * value + last_d);
        last_d = _d;
        numerator = Math.ceil(original_value * denominator)

        if (Math.abs(numerator/denominator - original_value) < tol)
            break;
        iteration++;
    }
    return {numerator: numerator, denominator: denominator};
};

Answer 4

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 ]

Answer 5

There is a very simple solution using string representation of numbers

    string = function(f){ // returns string representation of an object or number
        return f+"";
    }
    fPart = function(f){ // returns the fraction part (the part after the '.') of a number
        str = string(f);
        return str.indexOf(".")<0?"0":str.substring(str.indexOf(".") + 1);
    }
    wPart = function(f){ // returns the integer part (the part before the '.') of a number
        str = string(f);
        return str.indexOf(".")<0?str:str.substring(0, str.indexOf(".")); // possibility 1
        //return string(f - parseInt(fPart(f))); // just substract the fPart
    }

    power = function(base, exp){
        var tmp = base;
        while(exp>1){
            base*=tmp;
            --exp;
        }
        return base;
    }

    getFraction = function(f){ // the function
        var denominator = power(10, fPart(f).length), numerator = parseInt(fPart(f)) + parseInt(wPart(f))*denominator;
        return "[ " + numerator + ", " + denominator + "]";
    }

    console.log(getFraction(987.23));

which will just check how many numbers are in the fraction and then expands the fraction of f/1 until f is an integer. This can lead to huge fractions, so you can reduce it by dividing both numerator and denominator by the greatest common divisor of both, e.g.

    // greatest common divisor brute force
    gcd = function(x,y){
        for(var i = Math.min(x, y);i>0;i--) if(!(x%i||y%i)) return i;
        return 1;
    }

Answer 6

The good news is that it's possible, but you'll have to convert it to code.

Let's go with 2.56 for no reason at all.

Use the decimal portion of the number .56

There are 2 digits in .56, write .56 as 56/100.

So we have 2 + 56/100 and need to reduce this fraction to lowest terms by dividing both the numerator and denominator by the greatest common divisor, which is 4 in this case.

So, this fraction reduced to lowest terms is 2 + 14/25.

To add those whole 2, we multiply by the divisor and add to the 14

(2*25 + 14)/25 = 64/25