Why 0.1+0.2==0.3 False?

#javascript #tutorial #beginners #codenewbie

Hello Everyone today i will be discussing this famous question
Why 0.1 + 0.2 === 0.3 is false?

Let's get started...

I am using Javascript to show this but this comparison of floating point can be seen in other programming languages as well where they also return false for this comparison.

Code Example -

console.log(0.1 + 0.2 === 0.3)
//output - false

It returned false but 0.1 + 0.2 = 0.3 then it why it didn't returned true?
Well These floating point numbers cannot be precisely represented in Base 2 floating point number.This Explaination of base 2 concept is quite complicated to show but i will show you the simple reason why it happened.

console.log(0.1 + 0.2)
// output - 0.30000000000000004

The actual output of those 2 numbers is 0.30000000000000004 that's why it returned false because we are comparing this

console.log(0.3 === 30000000000000004)
// false

Now you understand why it returned false.

console.log(0.1 + 0.2 === 0.30000000000000004)
//output - true

This time it will return true

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Top comments (4)

JoelBonetR 🥇 • Aug 29 '22 • Edited

That's a recurring topic, and the reasons behind are quite interesting to me, if I must, let me add the complex stuff, I already tried to explain it in this comment -as best as I could and with the help of some guys from SO- that i'm copy-pasting because it doesn't let me embed it:

Just remember that is not a "Javascript issue" but an issue of the binary base we have most of the time.

In most programming languages, floating point numbers are represented a lot like scientific notation: with an exponent and a mantissa or significand.

A very simple number, say 9.2, is actually this fraction:
5179139571476070 * 2^-49
Where the exponent is -49 and the mantissa or significand is 5179139571476070.

The reason it is impossible to represent some decimal numbers this way is that both the exponent and the mantissa must be integers. In other words, all floats must be an integer multiplied by an integer power of 2.

9.2 may be simply 92/10, but 10 cannot be expressed as 2n if n is limited to integer values (2³=8 and 2⁴=16).

This is information gathered from a pair of comments in SO with some annotations added in a vague try to make it more understandable, because honestly I don't feel myself skilled enough on this mathematical topics to explain it by my own without spending days in previous research and doing diagrams, examples and so.

You can check the original comments here.