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## JavaScript Numbers

#### Numbers can be written with, or without, decimals.

JavaScript Numbers

JavaScript numbers can be written with, or without decimals:

Example

var x = 34.00;    // A number with decimals
var y = 34;       // A number without decimals

Extra large or extra small numbers can be written with scientific (exponent) notation:

Example

var x = 123e5;    // 12300000
var y = 123e-5;   // 0.00123

JavaScript Numbers are Always 64-bit Floating Point

Unlike many other programming languages, JavaScript does not define different types of numbers, like integers, short, long, floating-point etc.

JavaScript numbers are always stored as double precision floating point numbers, following the international IEEE 754 standard.

This format stores numbers in 64 bits, where the number (the fraction) is stored in bits 0 to 51, the exponent in bits 52 to 62, and the sign in bit 63:

Value (aka Fraction/Mantissa) Exponent Sign
52 bits (0 - 51)  11 bits (52 - 62) 1 bit (63)

Precision

Integers (numbers without a period or exponent notation) are considered accurate up to 15 digits.

Example

var x = 999999999999999;   // x will be 999999999999999
var y = 9999999999999999// y will be 10000000000000000

The maximum number of decimals is 17, but floating point arithmetic is not always 100% accurate:

Example

var x = 0.2 + 0.1;         // x will be 0.30000000000000004

To solve the problem above, it helps to multiply and divide:

Example

var x = (0.2 * 10 + 0.1 * 10) / 10;       // x will be 0.3

JavaScript interprets numeric constants as hexadecimal if they are preceded by 0x.

Example

var x = 0xFF;             // x will be 255

Never write a number with a leading zero (like 07). Some JavaScript versions interpret numbers as octal if they are written with a leading zero.

By default, Javascript displays numbers as base 10 decimals.

But you can use the toString() method to output numbers as base 16 (hex), base 8 (octal), or base 2 (binary).

Example

var myNumber = 128;
myNumber.toString(16);     // returns 80
myNumber.toString(8);      // returns 200
myNumber.toString(2);      // returns 10000000

Infinity

Infinity (or -Infinity) is the value JavaScript will return if you calculate a number outside the largest possible number.

Example

var myNumber = 2;
while (myNumber != Infinity) {          // Execute until Infinity
myNumber = myNumber * myNumber;
}

Division by 0 (zero) also generates Infinity:

Example

var x =  2 / 0;          // x will be Infinity
var y = -2 / 0;          // y will be -Infinity

Infinity is a number: typeOf Infinity returns number.

Example

typeof Infinity;        // returns "number"

NaN - Not a Number

NaN is a JavaScript reserved word indicating that a value is not a number.

Trying to do arithmetic with a non-numeric string will result in NaN (Not a Number):

Example

var x = 100 / "Apple" // x will be NaN (Not a Number)

However, if the string contains a numeric value , the result will be a number:

Example

var x = 100 / "10";     // x will be 10

You can use the global JavaScript function isNaN() to find out if a value is a number.

Example

var x = 100 / "Apple";
isNaN(x);               // returns true because x is Not a Number

Watch out for NaN. If you use NaN in a mathematical operation, the result will also be NaN:

Example

var x = NaN;
var y = 5;
var z = x + y;         // z will be NaN

Or the result might be a concatenation:

Example

var x = NaN;
var y = "5";
var z = x + y;         // z will be NaN5

NaN is a number, and typeof NaN returns number:

Example

typeof NaN;             // returns "number"

Numbers Can be Objects

Normally JavaScript numbers are primitive values created from literals: var x = 123

But numbers can also be defined as objects with the keyword new: var y = new Number(123)

Example

var x = 123;
var y = new Number(123);

// typeof x returns number
// typeof y returns object

Do not create Number objects. It slows down execution speed. The new keyword complicates the code. This can produce some unexpected results:

When using the == equality operator, equal numbers looks equal:

Example

var x = 500;
var y = new Number(500);

// (x == y) is true because x and y have equal values

When using the === equality operator, equal numbers are not equal, because the === operator expects equality in both type and value.

Example

var x = 500;
var y = new Number(500);

// (x === y) is false because x and y have different types

Or even worse. Objects cannot be compared:

Example

var x = new Number(500);
var y = new Number(500);

// (x == y) is false because objects cannot be compared

JavaScript objects cannot be compared.

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