# Converting Decimals to Fractions with JavaScript - Simplify & Improve

I wrote a simple script that converts a decimal to a mixed number, proper, or improper fraction depending on the inputed decimal.

It works but I think it could be improved as it hangs when large decimals are used. Please review and let me know how I could improve and simplify it. Thanks.

My script on JS Bin: http://jsbin.com/axulob/1/edit

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
<title>Untitled Document</title>
<script>
window.onload = function() {

var factor;

// Finds the highest common factor of 2 numbers
function highestCommonFactor() {
for (factor = numerator; factor > 0; factor--) {
if ((numerator % factor == 0) && (denominator % factor == 0)) {
return factor;
}
}
}

// Enter a decimal to convert to a fraction
var decimal = "1.75";

// Split the decimal
var decimalArray = decimal.split(".");

var leftDecimalPart = decimalArray[0];
var rightDecimalPart = decimalArray[1];

// Save decimal part only for later use
var decimalOnly = "0." + rightDecimalPart;

// Find the decimal multiplier
var multiplier = "1";

for (var i = 0; i < rightDecimalPart.length; i++) {
multiplier += "0";
}

// Create numerator by multiplying the multiplier and decimal part together
var numerator = Number(multiplier) * Number(decimalOnly);

var denominator = multiplier;

// Find the highest common factor for the numerator and denominator
highestCommonFactor();

// Simplify the fraction by dividing the numerator and denominator by the factor
var numerator = Number(numerator) / Number(factor);
var denominator = Number(denominator) / Number(factor);

// Output as a mixed number fraction (depending on input)
var mixedNumber = leftDecimalPart + " " + numerator + "/" + denominator;

// Output as a proper fraction or improper fraction (depending on input)
var numerator = numerator + (leftDecimalPart * denominator);
var fraction = numerator + "/" + denominator;

// Display solution
document.getElementById("divSolution").innerText = fraction;
}
</script>

<body>
<div id="divSolution"></div>
</body>
</html>


1. highestCommonFactor should take 2 integers as parameter instead of relying on the variable numerator and denominator'. Also, you could find it using Euclid'a algorithm.

2. I am wrong is saying that this piece of code :

var rightDecimalPart = decimalArray[1];
// Save decimal part only for later use
var decimalOnly = "0." + rightDecimalPart;
// Find the decimal multiplier
var multiplier = "1";
for (var i = 0; i < rightDecimalPart.length; i++) {
multiplier += "0";
}
// Create numerator by multiplying the multiplier and decimal part together
var numerator = Number(multiplier) * Number(decimalOnly);


is here to transform a number such as 78924 in 0.78924 and then check that have to multiply it by 100000 to get an integer which is ... 78924.

Edit After a first cleanup, I get :

function highestCommonFactor(a,b) {
if (b==0) return a;
return highestCommonFactor(b,a%b);
}

var decimal = "1.75";
var decimalArray = decimal.split(".");
var leftDecimalPart = decimalArray[0];
var rightDecimalPart = decimalArray[1];

var denominator = "1";

for (var i = 0; i < rightDecimalPart.length; i++) {
denominator += "0";
}
document.getElementById("debug").innerText = denominator;
var factor = highestCommonFactor(rightDecimalPart, denominator);

// Simplify the fraction by dividing the numerator and denominator by the factor
var denominator = Number(denominator) / Number(factor);
var numerator = (Number(rightDecimalPart) / Number(factor)) + (leftDecimalPart * denominator);

// Display solution as a proper fraction or improper fraction (depending on input)
document.getElementById("divSolution").innerText = numerator + "/" + denominator;


I'll try to go a step further.

Edit 2 After a rewriting of the calculation, here's what I got :

function highestCommonFactor(a,b) {
if (b==0) return a;
return highestCommonFactor(b,a%b);
}

var decimal = "1.75";
var decimalArray = decimal.split(".");
var leftDecimalPart = decimalArray[0]; // 1
var rightDecimalPart = decimalArray[1]; // 75

var numerator = leftDecimalPart + rightDecimalPart // 175
var denominator = Math.pow(10,rightDecimalPart.length); // 100
var factor = highestCommonFactor(numerator, denominator); // 25
denominator /= factor;
numerator /= factor;

document.getElementById("divSolution").innerText = numerator + "/" + denominator;
`
• Thanks for taking the time to go through my code. Could you explain how the function highestCommonFactor works? – user1822824 Jan 8 '13 at 21:31
• I understand Euclid'a algorithm but I don't get how it's returning 2 values (return highestCommonFactor(b,a%b))? I assume it's multiplying (b) * ((a%b)). – user1822824 Jan 8 '13 at 22:39
• The method highestCommonFactor takes 2 (integer) arguments and return 1 (integer) value. I used the formula from en.wikipedia.org/wiki/… to write this recursive function. – SylvainD Jan 9 '13 at 0:23