In this tutorial, we will explain the JavaScript Number.EPSILON property. It represents the difference between 1 and the smallest floating-point number greater than 1. It exists because not all decimal numbers can be represented accurately and exactly in the binary system.

Table of Contents

## Floating-point precision problem

The computers use the binary system to store numbers and use the floating-point arithmetic, while in real-world we use the decimal system. Not all decimal numbers can be represented correctly in binary numbers.

For Example

`0.1`

when converted from decimal to binary results in `0.0001100110011001101`

. Now convert it back from binary to decimal will result in `0.1000003814697265625`

The above case is similar to how 1/3 ( 0.33333) cannot be represented as accurately in decimal.

The decimal 10 is represented as 1010 in binary. Now divide 1 by 1010 and you will find out that the division goes on forever just like 1/3.

Because of the above loss of precision occurs, the strange results like the following happens

1 2 3 4 5 6 7 8 9 10 | console.log(0.1 + 0.2); console.log(0.2 + 0.4); console.log(0.2 + 0.7); //output //0.30000000000000004 //0.6000000000000001 //0.8999999999999999 |

The difference is very minute, but this definitely causes a problem when you compare two results. For Example, the following results in `false`

rather than `true`

.

1 2 3 4 5 6 | console.log((0.1 + 0.2) ==.3); //output //false |

## Number.EPSILON

One of the ways in which to avoid such problems is to use a very small number as a tolerance for comparison. If the difference between the compared numbers is less than the tolerance, then they are considered equal.

The JavaScript provides `EPSILON`

static property of the Number object as predefined tolerance. It is the difference between 1 and the smallest floating-point number greater than 1.

1 2 3 4 5 6 | console.log(Number.EPSILON) //output //2.220446049250313e-16 |

If the difference between the two numbers is less than the `EPSILON`

, then they are considered equal.

1 2 3 4 5 6 7 | function numberEquals(x:number, y:number) { return Math.abs(x - y) < Number.EPSILON; } console.log(numberEquals(0.1 + 0.2, 0.3)); // true |

Number`.EPSILON`

is a non-writable, non-enumerable, and non-configurable property.

## Summary

The conversion from a decimal number to binary is not always accurate. It can result in loss of precision. It is evident when you compare two number (ex: `(0.1 + 0.2) ==.3`

), who are supposed to be equal but results in false. `Number.EPSILON`

is used as tolerance for the number comparison. If the difference between the numbers is less than the `Number.EPSILON`

, then they are considered equal.

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