Category Archives: math

Most Beautiful Equation in Mathematics

e to the pi i for dummies

More info:
Quora QA
Wikipedia

Larry Battle

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Ratio.js – Fractions for javascript

Hey Everyone,
I created a project called Ratio.js. Basically the goal of the project is to provide an simple object for dealing with fractions in javascript.
Check it out here and tell me what this.

Ratio.js

Sample Code

 
// converts decimal values into the form of a fraction.
a = Ratio.parse(1/2);
a.toString() == "1/2";
 
// converts strings in the form of "a/b" to a fraction a/b.
a = Ratio.parse( "1/2" );
a.toString() == "1/2";
 
var result = Ratio.parse( 12.12121212121212 ).reduce().toString();
result == "400/33";

Simple Demo

Larry Battle

I love to program, and discover new tech. Check out my stackoverflow and github accounts.

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How to convert a repeating decimal to a fraction


Here are 4 simple steps to convert a repeating decimal to a fraction.

Step 1: Check to see if the number has a repeating decimal. Stop if it doesn’t and do normal conversion.

Step 2: Split the decimal into 3 parts; i, x, r. Such that the decimal equals `i.x(r)*`.

Step 3: Create a fraction in the form `a/b`.
a = ((ixr as int) – (ix as int))
b = ((10^x.length)*(10^r.length – 1))

Step 4: (optional) Reduce the fraction by dividing by the greatest common denominator.

Example:
4/3 = 1.333… which sets i = “1”, x = “”, r = “3”.
a = (13 – 1) = 12, b = ((10^0)*(10^1 – 1)) = 9
a/b = 12 / 9 = 4/3

Ratio.js does this for you when the `reduce` function is called.

Example using Ratio.js:

Ratio.parse( "1/3" ).reduce().toString() === "1/3";
Ratio.parse( 4/3 ).reduce().toString() === "4/3";
Ratio.parse( 0.123451234512345 ).reduce().toString() === "4115/33333";
Ratio.parse( 0.987987989798979897 ).reduce().toString() === "978108109901/990000000000";

DEMO

Larry Battle

I love to program, and discover new tech. Check out my stackoverflow and github accounts.

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Code of the Day: Javascript Decimal Expansion a.k.a Division


Today’s Code of the Day is about decimal expansion, which is just division.

So you might be asking yourself, “if decimal expansion is divsion. Then why not use a/b?”.
Well the problem is that Javascript has a ton of problems when dealing with floating point operations because of the way they are stored.

Examples:

var a = 1/3;
a.toString()     // returns  "0.3333333333333333"
a.toFixed(25);   // returns "0.3333333333333333148296163"
0.1 + 0.2;       // returns 0.30000000000000004

Source for decimalExpansion()

// borrowed from jQuery 1.7.2
var isNumeric = function(val){
	return !isNaN(parseFloat(val)) && isFinite(val);
};
/**
* @author Larry Battle <http://bateru.com/news/contact-me>
* @date May 16, 2012
* @license MIT and GPLv3
*/
//decimalExpansion returns a string representation of a divided by b to a fixed length.
// All the paramaters must be whole numbers.
// Example: decimalExpansion( 1, 3, 3 ) === "0.333"
var decimalExpansion = function (top, bottom, decLength) {
	if (!isNumeric(top) || !isNumeric(bottom) || !isNumeric(decLength) || !bottom) {
		return null;
	}
	var sign = ((top * bottom) != Math.abs(top * bottom)) ? "-" : "";
	top = Math.abs(top);
	bottom = Math.abs(bottom);
	decLength = Math.abs(decLength);
 
	var result = Math.floor(top / bottom),
	remainder = top % bottom,
	maxDecimal = 100,
	i = Math.min(Math.max(0, decLength), maxDecimal) + 1;
 
	if (1 < i) {
		result += ".";
		while (i--) {
			top = remainder * 10;
			remainder = top % bottom;
			result += "" + Math.floor(top / bottom);
		}
		result = result.replace(/(\d)(\d)$/, function (match, a, b) {
				return +b > 4 ? +a + 1 : a;
			});
	}
	return sign + result;
};

Test cases:

Demo:

Here are excellent links over the topic.
Wolfram MathWorld: Decimal Expansion
Wikipedia.org: Fraction (mathematics)
Oracle: What Every Computer Scientist Should Know About Floating-Point Arithmetic

Larry Battle

I love to program, and discover new tech. Check out my stackoverflow and github accounts.

More Posts - Website

Follow Me:
Twitter