## Round to at most 2 decimal places (only if necessary)

### Question

I'd like to round at most 2 decimal places, but only if necessary.

Input:

``````10
1.7777777
9.1
``````

Output:

``````10
1.78
9.1
``````

How can I do this in JavaScript?

2020/01/08
1
2863
1/8/2020 11:41:01 PM

Use `Math.round(num * 100) / 100`

Edit: to ensure things like 1.005 round correctly, we use

`Math.round((num + Number.EPSILON) * 100) / 100`

2020/01/23
3655
1/23/2020 5:04:27 PM

You can use

``````function roundToTwo(num) {
return +(Math.round(num + "e+2")  + "e-2");
}
``````

I found this over on MDN. Their way avoids the problem with 1.005 that was mentioned.

``````roundToTwo(1.005)
1.01
roundToTwo(10)
10
roundToTwo(1.7777777)
1.78
roundToTwo(9.1)
9.1
roundToTwo(1234.5678)
1234.57
``````
2018/02/12

MarkG's answer is the correct one. Here's a generic extension for any number of decimal places.

``````Number.prototype.round = function(places) {
return +(Math.round(this + "e+" + places)  + "e-" + places);
}
``````

Usage:

``````var n = 1.7777;
n.round(2); // 1.78
``````

Unit test:

``````it.only('should round floats to 2 places', function() {

var cases = [
{ n: 10,      e: 10,    p:2 },
{ n: 1.7777,  e: 1.78,  p:2 },
{ n: 1.005,   e: 1.01,  p:2 },
{ n: 1.005,   e: 1,     p:0 },
{ n: 1.77777, e: 1.8,   p:1 }
]

cases.forEach(function(testCase) {
var r = testCase.n.round(testCase.p);
assert.equal(r, testCase.e, 'didn\'t get right number');
});
})
``````
2013/11/01

You should use:

``````Math.round( num * 100 + Number.EPSILON ) / 100
``````

No one seems to be aware of `Number.EPSILON`.

Also it's worth noting that this is not a JavaScript weirdness like some people stated.

That is simply the way floating point numbers works in a computer. Like 99% of programming languages, JavaScript doesn't have home made floating point numbers; it relies on the CPU/FPU for that. A computer uses binary, and in binary, there isn't any numbers like `0.1`, but a mere binary approximation for that. Why? For the same reason than 1/3 cannot be written in decimal: its value is 0.33333333... with an infinity of threes.

Here come `Number.EPSILON`. That number is the difference between 1 and the next number existing in the double precision floating point numbers. That's it: There is no number between `1` and 1 + `Number.EPSILON`.

EDIT:

As asked in the comments, let's clarify one thing: adding `Number.EPSILON` is relevant only when the value to round is the result of an arithmetic operation, as it can swallow some floating point error delta.

It's not useful when the value comes from a direct source (e.g.: literal, user input or sensor).

EDIT (2019):

Like @maganap and some peoples have pointed out, it's best to add `Number.EPSILON` before multiplying:

``````Math.round( ( num + Number.EPSILON ) * 100 ) / 100
``````

EDIT (december 2019):

Lately, I use a function similar to this one for comparing numbers epsilon-aware:

``````const ESPILON_RATE = 1 + Number.EPSILON ;
const ESPILON_ZERO = Number.MIN_VALUE ;

function epsilonEquals( a , b ) {
if ( Number.isNaN( a ) || Number.isNaN( b ) ) {
return false ;
}
if ( a === 0 || b === 0 ) {
return a <= b + EPSILON_ZERO && b <= a + EPSILON_ZERO ;
}
return a <= b * EPSILON_RATE && b <= a * EPSILON_RATE ;
}
``````

My use-case is an assertion + data validation lib I'm developing for many years.

In fact, in the code I'm using `ESPILON_RATE = 1 + 4 * Number.EPSILON` and `EPSILON_ZERO = 4 * Number.MIN_VALUE` (four times the epsilon), because I want an equality checker loose enough for cumulating floating point error.

So far, it looks perfect for me. I hope it will help.

2020/01/09

One can use `.toFixed(NumberOfDecimalPlaces)`.

``````var str = 10.234.toFixed(2); // => '10.23'
var number = Number(str); // => 10.23
``````
2017/05/18

This question is complicated.

Suppose we have a function, `roundTo2DP(num)`, that takes a float as an argument and returns a value rounded to 2 decimal places. What should each of these expressions evaluate to?

• `roundTo2DP(0.014999999999999999)`
• `roundTo2DP(0.0150000000000000001)`
• `roundTo2DP(0.015)`

The 'obvious' answer is that the first example should round to 0.01 (because it's closer to 0.01 than to 0.02) while the other two should round to 0.02 (because 0.0150000000000000001 is closer to 0.02 than to 0.01, and because 0.015 is exactly halfway between them and there is a mathematical convention that such numbers get rounded up).

The catch, which you may have guessed, is that `roundTo2DP` cannot possibly be implemented to give those obvious answers, because all three numbers passed to it are the same number. IEEE 754 binary floating point numbers (the kind used by JavaScript) can't exactly represent most non-integer numbers, and so all three numeric literals above get rounded to a nearby valid floating point number. This number, as it happens, is exactly

0.01499999999999999944488848768742172978818416595458984375

which is closer to 0.01 than to 0.02.

You can see that all three numbers are the same at your browser console, Node shell, or other JavaScript interpreter. Just compare them:

``````> 0.014999999999999999 === 0.0150000000000000001
true``````

So when I write `m = 0.0150000000000000001`, the exact value of `m` that I end up with is closer to `0.01` than it is to `0.02`. And yet, if I convert `m` to a String...

``````> var m = 0.0150000000000000001;
> console.log(String(m));
0.015
> var m = 0.014999999999999999;
> console.log(String(m));
0.015``````

... I get 0.015, which should round to 0.02, and which is noticeably not the 56-decimal-place number I earlier said that all of these numbers were exactly equal to. So what dark magic is this?

The answer can be found in the ECMAScript specification, in section 7.1.12.1: ToString applied to the Number type. Here the rules for converting some Number m to a String are laid down. The key part is point 5, in which an integer s is generated whose digits will be used in the String representation of m:

let n, k, and s be integers such that k ≥ 1, 10k-1s < 10k, the Number value for s × 10n-k is m, and k is as small as possible. Note that k is the number of digits in the decimal representation of s, that s is not divisible by 10, and that the least significant digit of s is not necessarily uniquely determined by these criteria.

The key part here is the requirement that "k is as small as possible". What that requirement amounts to is a requirement that, given a Number `m`, the value of `String(m)` must have the least possible number of digits while still satisfying the requirement that `Number(String(m)) === m`. Since we already know that `0.015 === 0.0150000000000000001`, it's now clear why `String(0.0150000000000000001) === '0.015'` must be true.

Of course, none of this discussion has directly answered what `roundTo2DP(m)` should return. If `m`'s exact value is 0.01499999999999999944488848768742172978818416595458984375, but its String representation is '0.015', then what is the correct answer - mathematically, practically, philosophically, or whatever - when we round it to two decimal places?

There is no single correct answer to this. It depends upon your use case. You probably want to respect the String representation and round upwards when:

• The value being represented is inherently discrete, e.g. an amount of currency in a 3-decimal-place currency like dinars. In this case, the true value of a Number like 0.015 is 0.015, and the 0.0149999999... representation that it gets in binary floating point is a rounding error. (Of course, many will argue, reasonably, that you should use a decimal library for handling such values and never represent them as binary floating point Numbers in the first place.)
• The value was typed by a user. In this case, again, the exact decimal number entered is more 'true' than the nearest binary floating point representation.

On the other hand, you probably want to respect the binary floating point value and round downwards when your value is from an inherently continuous scale - for instance, if it's a reading from a sensor.

These two approaches require different code. To respect the String representation of the Number, we can (with quite a bit of reasonably subtle code) implement our own rounding that acts directly on the String representation, digit by digit, using the same algorithm you would've used in school when you were taught how to round numbers. Below is an example which respects the OP's requirement of representing the number to 2 decimal places "only when necessary" by stripping trailing zeroes after the decimal point; you may, of course, need to tweak it to your precise needs.

``````/**
* Converts num to a decimal string (if it isn't one already) and then rounds it
* to at most dp decimal places.
*
* For explanation of why you'd want to perform rounding operations on a String
* rather than a Number, see http://stackoverflow.com/a/38676273/1709587
*
* @param {(number|string)} num
* @param {number} dp
* @return {string}
*/
function roundStringNumberWithoutTrailingZeroes (num, dp) {
if (arguments.length != 2) throw new Error("2 arguments required");

num = String(num);
if (num.indexOf('e+') != -1) {
// Can't round numbers this large because their string representation
// contains an exponent, like 9.99e+37
throw new Error("num too large");
}
if (num.indexOf('.') == -1) {
// Nothing to do
return num;
}

var parts = num.split('.'),
beforePoint = parts[0],
afterPoint = parts[1],
shouldRoundUp = afterPoint[dp] >= 5,
finalNumber;

afterPoint = afterPoint.slice(0, dp);
if (!shouldRoundUp) {
finalNumber = beforePoint + '.' + afterPoint;
} else if (/^9+\$/.test(afterPoint)) {
// If we need to round up a number like 1.9999, increment the integer
// before the decimal point and discard the fractional part.
finalNumber = Number(beforePoint)+1;
} else {
// Starting from the last digit, increment digits until we find one
// that is not 9, then stop
var i = dp-1;
while (true) {
if (afterPoint[i] == '9') {
afterPoint = afterPoint.substr(0, i) +
'0' +
afterPoint.substr(i+1);
i--;
} else {
afterPoint = afterPoint.substr(0, i) +
(Number(afterPoint[i]) + 1) +
afterPoint.substr(i+1);
break;
}
}

finalNumber = beforePoint + '.' + afterPoint;
}

// Remove trailing zeroes from fractional part before returning
return finalNumber.replace(/0+\$/, '')
}
``````

Example usage:

``````> roundStringNumberWithoutTrailingZeroes(1.6, 2)
'1.6'
> roundStringNumberWithoutTrailingZeroes(10000, 2)
'10000'
> roundStringNumberWithoutTrailingZeroes(0.015, 2)
'0.02'
> roundStringNumberWithoutTrailingZeroes('0.015000', 2)
'0.02'
> roundStringNumberWithoutTrailingZeroes(1, 1)
'1'
> roundStringNumberWithoutTrailingZeroes('0.015', 2)
'0.02'
> roundStringNumberWithoutTrailingZeroes(0.01499999999999999944488848768742172978818416595458984375, 2)
'0.02'
> roundStringNumberWithoutTrailingZeroes('0.01499999999999999944488848768742172978818416595458984375', 2)
'0.01'``````

The function above is probably what you want to use to avoid users ever witnessing numbers that they have entered being rounded wrongly.

(As an alternative, you could also try the round10 library which provides a similarly-behaving function with a wildly different implementation.)

But what if you have the second kind of Number - a value taken from a continuous scale, where there's no reason to think that approximate decimal representations with fewer decimal places are more accurate than those with more? In that case, we don't want to respect the String representation, because that representation (as explained in the spec) is already sort-of-rounded; we don't want to make the mistake of saying "0.014999999...375 rounds up to 0.015, which rounds up to 0.02, so 0.014999999...375 rounds up to 0.02".

Here we can simply use the built-in `toFixed` method. Note that by calling `Number()` on the String returned by `toFixed`, we get a Number whose String representation has no trailing zeroes (thanks to the way JavaScript computes the String representation of a Number, discussed earlier in this answer).

``````/**
* Takes a float and rounds it to at most dp decimal places. For example
*
*     roundFloatNumberWithoutTrailingZeroes(1.2345, 3)
*
* returns 1.234
*
* Note that since this treats the value passed to it as a floating point
* number, it will have counterintuitive results in some cases. For instance,
*
*     roundFloatNumberWithoutTrailingZeroes(0.015, 2)
*
* gives 0.01 where 0.02 might be expected. For an explanation of why, see
* http://stackoverflow.com/a/38676273/1709587. You may want to consider using the
*
* @param {number} num
* @param {number} dp
* @return {number}
*/
function roundFloatNumberWithoutTrailingZeroes (num, dp) {
var numToFixedDp = Number(num).toFixed(dp);
return Number(numToFixedDp);
}
``````
2017/06/01