Question

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, namely 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 amount of different numbers that can be represented is limited. For N decimal digits, the amount of numbers that can be represented is 10^N. Similarly, given 64 binary digits, you can represent 2⁶⁴ different numbers, which is about 18 quintillion (an 18 with 18 zeros after it). This is a lot.

Computer memory used to be a lot 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 amount of bits. Today, even personal computers have plenty of memory, so you are free to use 64-bit chunks, which means you need to worry about overflow only when dealing with truly astronomical numbers.

Not all whole numbers below 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 can also use scientific notation by adding an “e” (for “exponent”), followed by the exponent of the number:

2.998e8

That is 2.998 × 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 π (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.

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 . Remainder’s precedence is the same as that of multiplication and division. You’ll often see this operator referred to as modulo, though technically remainder is more accurate.

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. It isn’t mathematically solid, and it will quickly lead to our 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 precise, meaningful result.

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.