# wrong - How to deal with floating point number precision in JavaScript?

## tofixed javascript (20)

``````    You can use library https://github.com/MikeMcl/decimal.js/.
it will   help  lot to give proper solution.
javascript console output 95 *722228.630 /100 = 686117.1984999999
decimal library implementation
var firstNumber = new Decimal(95);
var secondNumber = new Decimal(722228.630);
var thirdNumber = new Decimal(100);
var partialOutput = firstNumber.times(secondNumber);
console.log(partialOutput);
var output = new Decimal(partialOutput).div(thirdNumber);
console.log(output.valueOf())== 686117.1985
``````

https://code.i-harness.com

I have the following dummy test script:

``````function test(){
var x = 0.1 * 0.2;
document.write(x);
}
test();
``````

This will print the result `0.020000000000000004` while it should just print `0.02` (if you use your calculator). As far as I understood this is due to errors in the floating point multiplication precision.

Does anyone have a good solution so that in such case I get the correct result `0.02`? I know there are functions like `toFixed` or rounding would be another possibility, but I'd like to really have the whole number printed without any cutting and rounding. Just wanted to know if one of you has some nice, elegant solution.

Of course, otherwise I'll round to some 10 digits or so.

0.6 * 3 it's awesome!)) For me this works fine:

``````function dec( num )
{
var p = 100;
return Math.round( num * p ) / p;
}
``````

Very very simple))

Are you only performing multiplication? If so then you can use to your advantage a neat secret about decimal arithmetic. That is that `NumberOfDecimals(X) + NumberOfDecimals(Y) = ExpectedNumberOfDecimals`. That is to say that if we have `0.123 * 0.12` then we know that there will be 5 decimal places because `0.123` has 3 decimal places and `0.12` has two. Thus if JavaScript gave us a number like `0.014760000002` we can safely round to the 5th decimal place without fear of losing precision.

For the mathematically inclined: http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

The recommended approach is to use correction factors (multiply by a suitable power of 10 so that the arithmetic happens between integers). For example, in the case of `0.1 * 0.2`, the correction factor is `10`, and you are performing the calculation:

``````> var x = 0.1
> var y = 0.2
> var cf = 10
> x * y
0.020000000000000004
> (x * cf) * (y * cf) / (cf * cf)
0.02
``````

A (very quick) solution looks something like:

``````var _cf = (function() {
function _shift(x) {
var parts = x.toString().split('.');
return (parts.length < 2) ? 1 : Math.pow(10, parts[1].length);
}
return function() {
return Array.prototype.reduce.call(arguments, function (prev, next) { return prev === undefined || next === undefined ? undefined : Math.max(prev, _shift (next)); }, -Infinity);
};
})();

Math.a = function () {
var f = _cf.apply(null, arguments); if(f === undefined) return undefined;
function cb(x, y, i, o) { return x + f * y; }
return Array.prototype.reduce.call(arguments, cb, 0) / f;
};

Math.s = function (l,r) { var f = _cf(l,r); return (l * f - r * f) / f; };

Math.m = function () {
var f = _cf.apply(null, arguments);
function cb(x, y, i, o) { return (x*f) * (y*f) / (f * f); }
return Array.prototype.reduce.call(arguments, cb, 1);
};

Math.d = function (l,r) { var f = _cf(l,r); return (l * f) / (r * f); };
``````

In this case:

``````> Math.m(0.1, 0.2)
0.02
``````

I definitely recommend using a tested library like SinfulJS

Have a look at Fixed-point arithmetic. It will probably solve your problem, if the range of numbers you want to operate on is small (eg, currency). I would round it off to a few decimal values, which is the simplest solution.

I am not that much good at programming, but was really interested in this topic so I tried to understand how to solve that without using any libraries or scripts

``````var toAlgebraic = function(f1, f2) {
let f1_base = Math.pow(10, f1.split('.')[1].length);
let f2_base = Math.pow(10, f2.split('.')[1].length);
f1 = parseInt(f1.replace('.', ''));
f2 = parseInt(f2.replace('.', ''));

let dif, base;
if (f1_base > f2_base) {
dif = f1_base / f2_base;
base = f1_base;
f2 = f2 * dif;
} else {
dif = f2_base / f1_base;
base = f2_base;
f1 = f1 * dif;
}

return (f1 * f2) / base;
};

console.log(0.1 * 0.2);
console.log(toAlgebraic("0.1", "0.2"));
``````

you might need refactor this code, because I am not good at programming :)

I like Pedro Ladaria's solution and use something similar.

``````function strip(number) {
return (parseFloat(number).toPrecision(12));
}
``````

Unlike Pedros solution this will round up 0.999...repeating and is accurate to plus/minus one on the least significant digit.

Note: When dealing with 32 or 64 bit floats, you should use toPrecision(7) and toPrecision(15) for best results. See this question for info as to why.

I'm finding BigNumber.js meets my needs.

A JavaScript library for arbitrary-precision decimal and non-decimal arithmetic.

It has good documentation and the author is very diligent responding to feedback.

The same author has 2 other similar libraries:

Big.js

A small, fast JavaScript library for arbitrary-precision decimal arithmetic. The little sister to bignumber.js.

and Decimal.js

An arbitrary-precision Decimal type for JavaScript.

Here's some code using BigNumber:

``````\$(function(){

var product = BigNumber(.1).times(.2);
\$('#product').text(product);

var sum = BigNumber(.1).plus(.2);
\$('#sum').text(sum);

});``````
``````<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"></script>

<!-- 1.4.1 is not the current version, but works for this example. -->
<script src="http://cdn.bootcss.com/bignumber.js/1.4.1/bignumber.min.js"></script>

.1 &times; .2 = <span id="product"></span><br>
.1 &plus; .2 = <span id="sum"></span><br>``````

Output using the following function:

``````var toFixedCurrency = function(num){
var num = (num).toString();
var one = new RegExp(/\.\d{1}\$/).test(num);
var two = new RegExp(/\.\d{2,}/).test(num);
var result = null;

if(one){ result = num.replace(/\.(\d{1})\$/, '.\$10');
} else if(two){ result = num.replace(/\.(\d{2})\d*/, '.\$1');
} else { result = num*100; }

return result;
}

function test(){
var x = 0.1 * 0.2;
document.write(toFixedCurrency(x));
}

test();
``````

Pay attention to the output `toFixedCurrency(x)`.

Surprisingly, this function has not been posted yet although others have similar variations of it. It is from the MDN web docs for Math.round(). It's concise and allows for varying precision.

``````function precisionRound(number, precision) {
var factor = Math.pow(10, precision);
return Math.round(number * factor) / factor;
}
``````

console.log(precisionRound(1234.5678, 1)); // expected output: 1234.6

console.log(precisionRound(1234.5678, -1)); // expected output: 1230

``````var inp = document.querySelectorAll('input');
var btn = document.querySelector('button');

btn.onclick = function(){
inp[2].value = precisionRound( parseFloat(inp[0].value) * parseFloat(inp[1].value) , 5 );
};

//MDN function
function precisionRound(number, precision) {
var factor = Math.pow(10, precision);
return Math.round(number * factor) / factor;
}``````
``````button{
display: block;
}``````
``````<input type='text' value='0.1'>
<input type='text' value='0.2'>
<button>Get Product</button>
<input type='text'>``````

The round() function at phpjs.org works nicely: http://phpjs.org/functions/round

``````num = .01 + .06;  // yields 0.0699999999999
rnum = round(num,12); // yields 0.07
``````

This function will determine the needed precision from the multiplication of two floating point numbers and return a result with the appropriate precision. Elegant though it is not.

``````function multFloats(a,b){
var atens = Math.pow(10,String(a).length - String(a).indexOf('.') - 1),
btens = Math.pow(10,String(b).length - String(b).indexOf('.') - 1);
return (a * atens) * (b * btens) / (atens * btens);
}
``````

To avoid this you should work with integer values instead of floating points. So when you want to have 2 positions precision work with the values * 100, for 3 positions use 1000. When displaying you use a formatter to put in the separator.

Many systems omit working with decimals this way. That is the reason why many systems work with cents (as integer) instead of dollars/euro's (as floating point).

Try my chiliadic arithmetic library, which you can see here. If you want a later version, I can get you one.

Use Number(1.234443).toFixed(2); it will print 1.23

``````function test(){
var x = 0.1 * 0.2;
document.write(Number(x).toFixed(2));
}
test();
``````

You are looking for an `sprintf` implementation for JavaScript, so that you can write out floats with small errors in them (since they are stored in binary format) in a format that you expect.

Try javascript-sprintf, you would call it like this:

``````var yourString = sprintf("%.2f", yourNumber);
``````

to print out your number as a float with two decimal places.

You may also use Number.toFixed() for display purposes, if you'd rather not include more files merely for floating point rounding to a given precision.

You can use `parseFloat()` and `toFixed()` if you want to bypass this issue for a small operation:

``````a = 0.1;
b = 0.2;

a + b = 0.30000000000000004;

c = parseFloat((a+b).toFixed(2));

c = 0.3;

a = 0.3;
b = 0.2;

a - b = 0.09999999999999998;

c = parseFloat((a-b).toFixed(2));

c = 0.1;
``````

not elegant but does the job (removes trailing zeros)

``````var num = 0.1*0.2;