Javascript: Rounded numbers don't add up (33.3 + 33.3 + 33.3 = 99.89999999999999?)

Question

Consider this javascript that rounds to the nearest tenth, then totals the numbers together.

var log = function(key, value) {
  var li = document.createElement("li");
  li.appendChild(document.createTextNode(key + " = " + value)); 
  document.getElementById("results").appendChild(li); 
  };

var number1 = Math.round(10*33.333)/10; // gives 33.3
var number2 = Math.round(10*33.333)/10; // gives 33.3
var number3 = Math.round(10*33.333)/10; // gives 33.3

var totalOfAllNumbers = number1 + number2 + number3; //gives 99.89999999999999?

var totalOfAllRealNumbers = 33.3 + 33.3 + 33.3; //gives 99.9?

log("number1", number1);
log("number2", number2);
log("number3", number3);
log("totalOfAllNumbers", totalOfAllNumbers);

<ul id="results"></ul>

The numbers appear to be rounded, but the total doesn't add up to 99.9? Why?

What is the difference between the number entered as 33.3 manually, and the result of a division? Are they different types?

Answer 1

I hate to give a flippant response, but it gives that rounding error number "because JavaScript".

A slightly less flippant answer is that the engine tries to guess (as described by ECMA spec) the type at each step of the addition and somewhere in the type guessing algorithm, it guesses it's a double instead of a float (or vice versa) and that's when you see this type of precision loss. If numerical accuracy are critical to you, I suggest using a different programming language with saner and more predictable number types.

Edit:

For example consider python 2.7:

>>> a = round(10*33.333, 2)/10
>>> b = round(10*33.333, 2)/10
>>> c = round(10*33.333, 2)/10
>>> a + b + c
99.999

Or ruby:

2.1.2 :001 > a = (10*33.333).round(2)/10
 => 33.333
2.1.2 :002 > b = (10*33.333).round(2)/10
 => 33.333
2.1.2 :003 > c = (10*33.333).round(2)/10
 => 33.333
2.1.2 :004 > a + b + c
 => 99.999