# Convert a decimal number to a fraction / rational number

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"`.

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);
``````

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
``````

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 ]
``````

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};
};
``````

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;
}
``````

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

Have tried something like this?

``````<script type="texrt/javascript>
var cnum = 3.5,deno = 10000,neww;
neww = cnum * deno;
while(!(neww % 2 > 0) && !(deno % 2 > 0)){
neww = neww / 2;
deno = deno / 2;
}
while(!(neww % 3 > 0) && !(deno % 3 > 0)){
neww = neww / 3;
deno = deno / 3;
}
while(!(neww % 5 > 0) && !(deno % 5 > 0)){
neww = neww / 5;
deno = deno / 5;
}
while(!(neww % 7 > 0) && !(deno % 7 > 0)){
neww = neww / 7;
deno = deno / 7;
}
while(!(neww % 11 > 0) && !(deno % 11 > 0)){
neww = neww / 11;
deno = deno / 11;
}
while(!(neww % 13 > 0) && !(deno % 13 > 0)){
neww = neww / 13;
deno = deno / 13;
}
while(!(neww % 17 > 0) && !(deno % 17 > 0)){
neww = neww / 17;
deno = deno / 17;
}
while(!(neww % 19 > 0) && !(deno % 19 > 0)){
neww = neww / 19;
deno = deno / 19;
}
console.log(neww+"/"+deno);
</script>
``````

I did what popnoodles suggested and here it is

``````function FractionFormatter(value) {
if (value == undefined || value == null || isNaN(value))
return "";

function _FractionFormatterHighestCommonFactor(u, v) {
var U = u, V = v
while (true) {
if (!(U %= V)) return V
if (!(V %= U)) return U
}
}

var parts = value.toString().split('.');
if (parts.length == 1)
return parts;
else if (parts.length == 2) {
var wholeNum = parts[0];
var decimal = parts[1];
var denom = Math.pow(10, decimal.length);
var factor = _FractionFormatterHighestCommonFactor(decimal, denom)
return (wholeNum == '0' ? '' : (wholeNum + " ")) + (decimal / factor) + '/' + (denom / factor);
} else {
return "";
}
}
``````

This may be a little old but the code that was posted fails on 0 values I have fixed that error and will post the updated code below

``````//function to get highest common factor of two numbers (a fraction)
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

if(isNaN(whole) === true)
{
whole = "0";
}

if(isNaN(decimal) === true)
{
return ((whole==0)?"0" : whole);
}
else
{
return ((whole==0)?"0 " : whole+" ")+decimal/t+"/"+num/t;
}
}
``````

I just want a leave one alternative that I found to convert decimal numbers into fractions and reducing fractions, it's a JS library.

The library calls fraction.js, it was really helpful for me and save me a lot time and work. Hope can be useful to somebody else!

I know this is an old question, but I have created a function that has been greatly simplified.

``````Math.fraction=function(x){
return x?+x?x.toString().includes(".")?x.toString().replace(".","")/(function(a,b){return b?arguments.callee(b,a%b):a;})(x.toString().replace(".",""),"1"+"0".repeat(x.toString().split(".")[1].length))+"/"+("1"+"0".repeat(x.toString().split(".")[1].length))/(function(a,b){return b?arguments.callee(b,a%b):a;})(x.toString().replace(".",""),"1"+"0".repeat(x.toString().split(".")[1].length)):x+"/1":NaN:void 0;
}
``````

Call it with `Math.fraction(2.56)`

It will:

• return NaN if the input is not a number
• return undefined if the input is undefined
• reduce the fraction
• return a `string` (use `Math.fraction(2.56).split("/")` for an array containing the numerator and denominator)

Please note that this uses the deprecated `arguments.callee`, and thus may be incompatible in some browsers.

Test it here