convert decimal number to fraction in javascript or closest fraction

Question

So i want to be able to convert any decimal number into fraction. In both forms such as one without remainder like this: 3/5 or with remainder: 3 1/4.

what i was doing is this..

lets say i have number .3435.

Calculate amount of digits after decimals.
multiply by 10 with power of the amount before number.
then somehow find greatest common factor.

Now i don't know how to find GCF. And nor i know how to implement logic to find fraction that represents a number closely or in remainder form if exact fraction doesn't exists.

code i have so far: (testing)

x = 34/35;
a = x - x.toFixed();
tens = (10).pow(a.toString().length - 2);

numerator = tens * x;
denominator = tens;

Something like http://www.mathsisfun.com/converting-decimals-fractions.html — Xotic750, May 09 '14 at 23:15
Then take a look at something like [fraction.js](https://github.com/ekg/fraction.js) — Xotic750, May 09 '14 at 23:27
The major problem that you *will* face is that floating point numbers *cannot* handle values exactly (unless said values happen to be powers of two or sums thereof). — Niet the Dark Absol, May 09 '14 at 23:53
https://github.com/infusion/Fraction.js/ is worth a look too — Douglas, Aug 23 '19 at 20:34

score 28 · Accepted Answer · edited Feb 01 '19 at 17:41

28

Your first 2 steps are reasonable.

But what you should do is for the numerator and denominator calculate the Greatest Common Divisor (GCD) and then divide the numerator and denominator with that divisor to get the fraction you want.

GCD is rather easy to calculate. Here is Euclid's algorithm:

var gcd = function(a, b) {
  if (!b) return a;

  return gcd(b, a % b);
};

Edit

I've added a fully working JSFiddle.

edited Feb 01 '19 at 17:41

mega6382

8,889
16
47
67

answered May 09 '14 at 23:23

Sani Singh Huttunen

22,737
5
69
76

What do you get with 0.3435? – Xotic750 May 09 '14 at 23:45
@Xotic750: Obviously there needs to be a limit check since the nature of fractions. Something like `if (b < 0.0000001) return a;` but the theory is still sound. – Sani Singh Huttunen May 10 '14 at 00:03
I updated his fiddle with some stuff that gives correct answer http://jsfiddle.net/5QrhQ/3/. – Muhammad Umer May 10 '14 at 00:06
@SaniHuttunen I wasn't knocking the theory or your answer, I was just pointing out the fact that there are other things to consider, and using someone else's efforts may be a more effective solution, unless you are doing this as some kind of learning. :) – Xotic750 May 10 '14 at 00:09
what do you think of it now? – Muhammad Umer May 10 '14 at 00:11
@Xotic750: Yes. You should always try not to reinvent the wheel but as you pointed out this is probably for learning. – Sani Singh Huttunen May 10 '14 at 00:12
@MuhammadUmer: `parseInt` is one way to go. Another is [`Math.floor`](http://jsfiddle.net/5QrhQ/5/). – Sani Singh Huttunen May 10 '14 at 00:13
@SaniSinghHuttunen Answer is Simple, Aesthetic and Perfect – 10011101111 May 27 '18 at 06:03
Doesn't work as well with negative decimals. For example fraction of -3.00001 results in -4/1 and of -3.0000 in -3/1. – Pawel Kam Mar 25 '20 at 18:38
2/6 returns something weired either: 333333333333333/1000000000000000 - due to insanitized digital representation.... – Xerix Dec 18 '20 at 06:08

score 14 · Answer 2 · answered May 09 '14 at 23:50

14

Unless you are willing to work on developing something yourself then I would suggest using a library that someone has already put effort into, like fraction.js

Javascript

var frac = new Fraction(0.3435);

console.log(frac.toString());

Output

687/2000

On jsFiddle

answered May 09 '14 at 23:50

Xotic750

21,928
8
53
76

It seems like this one doesn't work with trailing digits decimals – Ricardo Metring Mar 19 '20 at 16:01

Stephen Quan · Answer 3 · 2020-01-23T23:20:30.030

You can use brute force test on different denominators and retain the result that has least error.

The algorithm below is an example of how you might go about this, but, suffers from being inefficient and limited to searching for denominators up to 10000.

function find_rational( value, maxdenom ) {
  console.clear();
  console.log( "Looking up: " + value );
  let best = { numerator: 1, denominator: 1, error: Math.abs(value - 1) }
  if ( !maxdenom ) maxdenom = 10000;
  for ( let denominator = 1; best.error > 0 && denominator <= maxdenom; denominator++ ) {
    let numerator = Math.round( value * denominator );
    let error = Math.abs( value - numerator / denominator );
    if ( error >= best.error ) continue;
    best.numerator = numerator;
    best.denominator = denominator;
    best.error = error;
    console.log( "Intermediate result: "
                   + best.numerator + "/" + best.denominator
                   + " (" + ( best.numerator/best.denominator)
                   + " error " + best.error + " )" );
  }
  console.log( "Final result: " + JSON.stringify( best ) );
  return best;
}
  
function calc() {
    const value = parseFloat( $("#myInput").val() );
    if ( isNaN(value) ) {
        $( "#myResult" ).val( "NaN" );
        return;
    }
    const rational = find_rational( value, 10000 );
    $("#myResult").val( rational.numerator
                        + " / " + rational.denominator
                        + " ( Error: " + rational.error + " )" );
}

calc();

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<P>
Enter a decimal number:<BR/>
<INPUT type="text" name="myInput" id="myInput" value=".3435" onkeyup="calc()"/><BR/>
</P>

<P>
Resulting Rational:<BR/>
<INPUT name="myResult" id="myResult" value=""/><BR/>
</P>

The above determines the .3435 as a fraction is 687 / 2000.

Also, had you gave it PI (e.g. 3.1415926) it produces good looking fractions like 22/7 and 355/113.

don't you think this maybe a little bit inefficient way to do it. — Muhammad Umer, May 10 '14 at 00:10
I did say it was inefficient, nevertheless, it is a simple answer. — Stephen Quan, May 10 '14 at 00:15
This is the actual best answer! It can correctly convert `0.5555555555555555` to `"5/9"`. Other answers cannot do that. — Happypig375, Jan 22 '17 at 04:30

score 9 · Answer 4 · answered Aug 08 '18 at 01:42

9

One quick and easy way of doing it is

getFraction = (decimal) => {
  for(var denominator = 1; (decimal * denominator) % 1 !== 0; denominator++);
  return {numerator: decimal * denominator, denominator: denominator};
}

answered Aug 08 '18 at 01:42

rman

125
1
6

`getFraction(0.003076991306616206)` takes over 10 seconds, but it works well enough – bryc Jun 20 '20 at 17:18

chowey · Answer 5 · 2020-05-10T05:00:09.630

8

I get very poor results using the GCD approach. I got much better results using an iterative approach.

For example, here is a very crude approach that zeros in on a fraction from a decimal:

function toFraction(x, tolerance) {
    if (x == 0) return [0, 1];
    if (x < 0) x = -x;
    if (!tolerance) tolerance = 0.0001;
    var num = 1, den = 1;

    function iterate() {
        var R = num/den;
        if (Math.abs((R-x)/x) < tolerance) return;

        if (R < x) num++;
        else den++;
        iterate();
    }

    iterate();
    return [num, den];
}

The idea is you increment the numerator if you are below the value, and increment the denominator if you are above the value.

edited May 10 '20 at 05:00

answered Feb 23 '18 at 18:05

chowey

8,318
6
49
77

man, you are awesome, all other failed except yours... – Rishad Baniya Feb 27 '21 at 07:13
Should be rewritten to avoid recursion to boost performance – PsychoX Nov 27 '21 at 01:04
Iterative approach (with benchmark to compare) posted in my answer below. – PsychoX Nov 27 '21 at 01:37
Actually, why is it `Math.abs((R-x)/x) < tolerance` instead of `Math.abs(R-x) < tolerance`? – PsychoX Nov 27 '21 at 03:04
1

`tolerance` as I defined it would be the "relative tolerance". `tolerance` as you defined it would be the "absolute tolerance". If absolute tolerance is fine for your application, then you can use it. – chowey Nov 27 '21 at 17:31

Dehan · Answer 6 · 2017-08-19T21:51:33.100

Use the Euclidean algorithm to find the greatest common divisor.

function reduce(numerator,denominator){
  var gcd = function gcd(a,b){
    return b ? gcd(b, a%b) : a;
  };
  gcd = gcd(numerator,denominator);
  return [numerator/gcd, denominator/gcd];
}

This will provide you with the following results on your console

reduce(2,4);
// [1,2]

reduce(13427,3413358);
// [463,117702]

So by continuing from already what you have,

var x = 34/35;
var a = x - x.toFixed();
var tens = Math.pow(10,a.toString().length - 2);

var numerator = tens * x;
var denominator = tens;

reduce(numerator,denominator);

Source: https://stackoverflow.com/a/4652513/1998725

kennebec · Answer 7 · 2014-05-10T17:38:38.473

The tricky bit is not letting floating points get carried away.

Converting a number to a string restrains the trailing digits,

especially when you have a decimal with an integer, like 1.0625.

You can round off clumsy fractions, by passing a precision parameter.

Often you want to force a rounded value up, so a third parameter can specify that.

(e.g.; If you are using a precision of 1/64, the smallest return for a non-zero number will be 1/64, and not 0.)

Math.gcd= function(a, b){
    if(b) return Math.gcd(b, a%b);
    return Math.abs(a);
}
Math.fraction= function(n, prec, up){
    var s= String(n), 
    p= s.indexOf('.');
    if(p== -1) return s;

    var i= Math.floor(n) || '', 
    dec= s.substring(p), 
    m= prec || Math.pow(10, dec.length-1), 
    num= up=== 1? Math.ceil(dec*m): Math.round(dec*m), 
    den= m, 
    g= Math.gcd(num, den);

    if(den/g==1) return String(i+(num/g));

    if(i) i= i+' and  ';
    return i+ String(num/g)+'/'+String(den/g);
}

Math.roundFraction(.3435,64); value: (String) 11/32

score 2 · Answer 8 · edited Oct 26 '19 at 08:48

2

I had researched all over the website and I did combine all code into one, Here you go!

function fra_to_dec(num){
    var test=(String(num).split('.')[1] || []).length;
    var num=(num*(10**Number(test)))
    var den=(10**Number(test))
    function reduce(numerator,denominator){
        var gcd = function gcd(a,b) {
            return b ? gcd(b, a%b) : a;
        };
        gcd = gcd(numerator,denominator);
        return [numerator/gcd, denominator/gcd];
    }
    return (reduce(num,den)[0]+"/"+reduce(num,den)[1])
}

This code is very easy to use! You can even put number in this function!

edited Oct 26 '19 at 08:48

N'Bayramberdiyev

5,636
7
23
43

answered Oct 26 '19 at 08:17

Carter Swinney

21
1

hey there seems to be a lot going on, i'd love some comments on overall steps taking places thanks – Muhammad Umer Oct 26 '19 at 14:14

score 1 · Answer 9 · answered Sep 06 '17 at 16:27

1

I came up with this for 16ths

function getfract(theNum){
    var input=theNum.toString();
    var whole = input.split(".")[0];
    var rem = input.split(".")[1] * .1;
    return(whole + " " + Math.round(rem * 16) + "/16");
}

answered Sep 06 '17 at 16:27

Jeff Price

49
1

score 1 · Answer 10 · answered Nov 23 '20 at 06:07

This is the fastest one I've got. No GCD. Good for at least 5 trailing decimals.

function decToFrac(n)
{
    let rcp = (n%1 == 0) ? 1: 1/(n%1);
    let den = rcp;
    const lim = 10;
    for (let i = 0; i < lim && Number.isInteger(Math.round(rcp * 10**(lim-i)) / 10**(lim-i)) != true; i++)
    {
        rcp = 1/(rcp%1);
        den *= rcp;
    }
    return [Math.round(n*den), Math.round(den)];
}

function impToProp(n, d)
{
    return [Math.floor(n/d), (n%d), d];
}

var dec = 3.141592;
var frac = decToFrac(dec); // improper
var prop = impToProp(frac[0], frac[1]); // proper

PsychoX · Answer 11 · 2021-11-27T02:08:02.367

Inspired by @chowey answer, which contained recursive implementation of finding close fraction for a decimal value within given tolerance, here is better (see benchmark), iterative version of it.

function toFractionIterative(x, epsilon = 0.0001) {
    if (x == 0) return [0, 1];
    const a = Math.abs(x);
    let n = 0;
    let d = 1;
    let r;
    while (true) {
        r = n / d;
        if (Math.abs((r - a) / a) < epsilon) {
            break;
        }
        if (r < a) {
            n++;
        }
        else {
            d++;
        }
    }
    return [x < 0 ? -n : n, d];
}

Benchmark (tl;dr: recursive 1,589 ops/s, iterative 5,955 ops/s; use iterative approach)

score 0 · Answer 12 · edited Dec 06 '21 at 09:50

function decimalToFraction(num) {
    let numsAfterDecPoint = num.toString().split('.')[1] ? num.toString().split('.')[1].length : 0;

    let numerator = num * Math.pow(10, numsAfterDecPoint);
    let denominator = Math.pow(10, numsAfterDecPoint);

    console.log(numerator + " / " + denominator)

    let d = GCD(numerator,denominator)

    return numerator / d + " / " + denominator / d

}

console.log(decimalToFraction(0.5)); // 5 / 10 => 1 / 2

console.log(decimalToFraction(178.45)); // 17845 / 100 => 3569 / 20

function GCD(a,b) {
    let r = 0;

    while(b != 0) {
        r = a % b 
        a = b;
        b = r;
    }

    return a;
}

convert decimal number to fraction in javascript or closest fraction

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