Secrets of numbers in JS

Rounding errors

Interesting things could happen in Javascript if you don't know how it's working under the hood. For example, floating-point numbers cause some rounding errors. 0.1 and 0.2 cannot be represented precisely. Hence, 0.1 + 0.2 === 0.3 yields false.

So, why it's happening? Javascript uses 32-bit floating-point number system. Representing many decimals in binary requires an infinite number of digits. Trying to calculate 0.1 (1/10) results in an indefinite number of decimal points. The result of 0.1 + 0.2 is 0.30000000000000004 which doesn't equal 0.3.

Number.EPSILON

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

function numberEquals(x: number, y: number) {
    return Math.abs(x - y) < Number.EPSILON;
}

numberEquals(0.1 + 0.2, 0.3); // true

The difference between 0.1 + 0.2 and 0.3 will be smaller than Number.EPSILON.

Double dots

Numbers can be transformed into strings with a fixed number of decimal points. If you'll call toFixed() function directly on an integer, you'll need to use double dots notation like this: 5..toFixed(1) === '5.0'. Why should you do it? Simply because the first dot notation is for representing floating-point numbers: 0.77.toFixed(1) === '0.7'
You can use toFixed() function in the previous example to match equality (0.1 + 0.2).toFixed(1) === 0.3.toFixed(1)

Quick note: Primitives in Javascript aren't objects, but why can you use "string".length, 0.77.toFixed(1)? Well, Javascript creates a special wrapper object with a value for the primitive when you call a method and deletes it then after execution.

Minimums, maximums

Number contains interesting constants which represent maximum and minimum integers and floating-point numbers. Javascript has Infinity and -Infinity, but they aren't real numbers.

Number.MAX_SAFE_INTEGER returns the largest integer. It's equal to 9007199254740991 And this expression is true:

Number.MAX_SAFE_INTEGER + 1 === Number.MAX_SAFE_INTEGER + 2; // true

Number.MAX_VALUE returns the largest floating-point number. It's equal to 1.7976931348623157e+308. Same expression for it:

Number.MAX_VALUE + 1.111 === Number.MAX_VALUE + 2.022; // true

Minimums are represented by Number.MIN_VALUE as the smallest floating-point number which is equal to 5e-324 and Number.MIN_SAFE_INTEGER which is equal to -9007199254740991.
Number.MIN_VALUE is also the closest floating point to zero.

Number.MIN_VALUE - 1 === -1; // true

Why is it true? Because this expression is similar to 0 - 1 === -1

Summary

Let's summarize the size of the Javascript numbers:

-Infinity < Number.MIN_SAFE_INTEGER < Number.MIN_VALUE < 0 < Number.MAX_SAFE_INTEGER < Number.MAX_VALUE < Infinity

When you're working with floating-point numbers, you should be careful and take into account rounding errors, because some numbers cannot be represented precisely. You can use third-party libraries or check differences between numbers with Number.EPSILON.

Photo by Volkan Olmez on Unsplash