*Why 0.1 + 0.2 == 0.3* is false in JS? Mystery Unsolved With Solution

JS follows a **32-bit floating point representation** for numbers.

Out of 32 bits :

**1** is **sign bit**(number is negative if the value is 1),

**8** bits indicate the **exponent** value(e) and other

**23** bits represent the **fraction** value.

With the 32 bits, the value is computed by this serious looking formula:

**With decimal fractions, this floating-point number system causes some rounding errors in JavaScript**. For example, 0.1 and 0.2 cannot be represented precisely. Hence, 0.1 + 0.2 === 0.3 yields false.

To really understand why 0.1 cannot be represented properly as a 32-bit floating-point number, you must understand binary. Representing many decimals in binary requires an infinite number of digits.This is because binary numbers are represented by 2 power n(2ˆn) where n is an integer. While trying to calculate 0.1, long division will go on forever.

Calculating 0.1 (1/10) results in an indefinite number of decimal points.

*Check the error rate while conversion from decimal to binary numbers in more depth at this **link*

*Now the question is can we solve this problem?*

— Yes. We can and We will.

We would use *Number.EPSILON** for this.*

**Number.EPSILON** returns the smallest interval between two representable numbers.This is useful for the problem with floating-point approximation.

STEPS INSIDE FUNCTIONafter numberEquals(0.1 + 0.2, 0.3) call:=Math.abs((0.1+0.2)-0.3) <Number.EPSILON

=Math.abs((0.30000000000000004)-0.3) <Number.EPSILON

=Math.abs((5.551115123125783e-17)-0.3) <Number.EPSILON

=Math.abs((5.551115123125783e-17)-0.3) <2.220446049250313e-16

Hence it returned “** true**”.

This function works by checking whether the difference between the two numbers are smaller than Number.EPSILON.

*Remember that Number.EPSILON is the smallest difference between two representable numbers**.*The difference between 0.1+0.2 and 0.3 will be smaller than Number.EPSILON.

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