# Numbers in JavaScript

Values of the number type are, unsurprisingly, numeric values. In a JavaScript program, they are written as follows:

13

Use that in a program, and it will cause the bit pattern for the number 13 to come into existence inside the computer’s memory.

JavaScript uses a fixed number of bits, 64 of them, to store a single num­ber value. There are only so many patterns you can make with 64 bits, which means that the number of different numbers that can be represented is lim­ited. With N decimal digits, you can represent 10N numbers. Similarly, given 64 binary digits, you can represent 264 different numbers, which is about 18 quintillion (an 18 with 18 zeros after it). That’s a lot.

Computer memory used to be much smaller, and people tended to use groups of 8 or 16 bits to represent their numbers. It was easy to accidentally overflow such small numbers—to end up with a number that did not fit into the given number of bits. Today, even computers that fit in your pocket have plenty of memory, so you are free to use 64-bit chunks, and you need to worry about overflow only when dealing with truly astronomical numbers.

Not all whole numbers less than 18 quintillion fit in a JavaScript num­ber, though. Those bits also store negative numbers, so one bit indicates the sign of the number. A bigger issue is that nonwhole numbers must also be represented. To do this, some of the bits are used to store the position of the decimal point. The actual maximum whole number that can be stored is more in the range of 9 quadrillion (15 zeros)—which is still pleasantly huge. Fractional numbers are written by using a dot.

9.81

For very big or very small numbers, you may also use scientific notation by adding an e (for exponent), followed by the exponent of the number.

2.998e8

That is 2.998 x 108 = 299,800,000.

Calculations with whole numbers (also called integers) smaller than the aforementioned 9 quadrillion are guaranteed to always be precise. Unfortu­nately, calculations with fractional numbers are generally not. Just as n (pi) cannot be precisely expressed by a finite number of decimal digits, many numbers lose some precision when only 64 bits are available to store them. This is a shame, but it causes practical problems only in specific situations. The important thing is to be aware of it and treat fractional digital numbers as approximations, not as precise values.

Arithmetic

The main thing to do with numbers is arithmetic. Arithmetic operations such as addition or multiplication take two number values and produce a new number from them. Here is what they look like in JavaScript:

100 + 4 * 11

The + and * symbols are called operators. The first stands for addition, and the second stands for multiplication. Putting an operator between two values will apply it to those values and produce a new value.

But does the example mean “add 4 and 100, and multiply the result by 11,” or is the multiplication done before the adding? As you might have guessed, the multiplication happens first. But as in mathematics, you can change this by wrapping the addition in parentheses.

(100 + 4) * 11

For subtraction, there is the – operator, and division can be done with the / operator.

When operators appear together without parentheses, the order in which they are applied is determined by the precedence of the operators. The example shows that multiplication comes before addition. The / operator has the same precedence as *. Likewise for + and -. When multiple operators with the same precedence appear next to each other, as in 1-2 + 1, they are applied left to right: (1 – 2) + 1.

These rules of precedence are not something you should worry about. When in doubt, just add parentheses.

There is one more arithmetic operator, which you might not immedi­ately recognize. The % symbol is used to represent the remainder operation. X % Y is the remainder of dividing X by Y. For example, 314 % 100 produces 14, and 144 % 12 gives 0. The remainder operator’s precedence is the same as that of multiplication and division. You’ll also often see this operator referred to as modulo.

Special Numbers

There are three special values in JavaScript that are considered numbers but don’t behave like normal numbers.

The first two are Infinity and -Infinity, which represent the positive and negative infinities. Infinity – 1 is still Infinity, and so on. Don’t put too much trust in infinity-based computation, though. It isn’t mathematically sound, and it will quickly lead to the next special number: NaN.

NaN stands for “not a number,” even though it is a value of the number type. You’ll get this result when you, for example, try to calculate 0/0 (zero divided by zero), Infinity – Infinity, or any number of other numeric opera­tions that don’t yield a meaningful result.

Source: Haverbeke Marijn (2018), Eloquent JavaScript: A Modern Introduction to Programming,

No Starch Press; 3rd edition.