Maths and comparison

Why it matters

Almost any program calculates something: an order total, the time until the lesson ends, game points, discount percentages. Programs also constantly compare: is there enough money, is the password right, is time up. This topic gives you all the tools for that.

Arithmetic

console.log(7 + 2);   // 9   addition
console.log(7 - 2);   // 5   subtraction
console.log(7 * 2);   // 14  multiplication
console.log(7 / 2);   // 3.5 division — a decimal!
console.log(7 % 2);   // 1   remainder
console.log(2 ** 10); // 1024 exponent

The order of operations is as in maths: first **, then *, /, %, then + and -. Parentheses change the order: (2 + 3) * 4 → 20, while 2 + 3 * 4 → 14.

The remainder %

A very useful operator:

• n % 2 === 0 — the number is even;
• n % 10 — the last digit of a number (1234 % 10 → 4);
• total % 60 — the minutes left over the full hours.

const seconds = 200;
console.log(Math.floor(seconds / 60), "min", seconds % 60, "sec");

Output:

3 min 20 sec

The Math object

Math is a built-in set of maths functions:

console.log(Math.round(4.5));  // 5   by normal rules
console.log(Math.floor(4.9));  // 4   down
console.log(Math.ceil(4.1));   // 5   up
console.log(Math.trunc(-4.7)); // -4  drop the fractional part
console.log(Math.max(3, 9, 2)); // 9
console.log(Math.min(3, 9, 2)); // 2
console.log(Math.abs(-8));     // 8   absolute value
console.log(Math.sqrt(81));    // 9   square root
console.log(Math.random());    // random from 0 to 1, e.g. 0.4271…

A random integer from 1 to 6 (a die): Math.floor(Math.random() * 6) + 1.

Decimals and precision

console.log(0.1 + 0.2);

Output:

0.30000000000000004

That's not a JavaScript bug — almost all languages store decimals like this. For money, count in cents (whole numbers) or round the result: Number((0.1 + 0.2).toFixed(2)) → 0.3. The toFixed(2) method returns a string with two digits after the point.

Comparison

A comparison gives a boolean value, true or false:

console.log(5 > 3);    // true
console.log(5 < 3);    // false
console.log(5 >= 5);   // true  greater than or equal
console.log(4 <= 3);   // false less than or equal
console.log(5 === 5);  // true  strictly equal
console.log(5 !== 3);  // true  not equal

Strict === and loose ==

console.log(5 === "5"); // false — different types
console.log(5 == "5");  // true  — == converts types first
console.log(0 == "");   // true  — surprise!

== tries to convert values to one type and gives strange results. Always use === and !==.

Strings are compared alphabetically, or more precisely by character codes: "apple" < "banana" → true, and "Z" < "a" → true, because capital letters come before lowercase ones.

How it works inside

All numbers in JavaScript are stored in one format — a 64-bit floating-point number (the IEEE 754 standard). That's why 7 / 2 gives 3.5 and not 3 as in some other languages, and why 0.1 + 0.2 isn't exactly 0.3: the decimal 0.1 can't be written exactly in binary, just as 1/3 can't be written exactly as a decimal. Division by zero doesn't break the program: 5 / 0 → Infinity.

Common mistakes

1. Expecting a whole number from division. 7 / 2 → 3.5. For a whole number — Math.floor(7 / 2).
2. = instead of ===. if (x = 5) doesn't compare, it assigns. Comparison is ===.
3. == instead of ===. 0 == "" → true. Write ===.
4. Rounding with the wrong function. Math.round — by the rules, Math.floor — down, Math.ceil — up. For "how many boxes are needed" — ceil; for "how many full hours" — floor.
5. toFixed returns a string. (1.5).toFixed(2) + 1 → "1.501". Wrap it in Number(...).

Cheat sheet

What	How
Operators	+ - * / % **
Remainder, evenness	n % 2 === 0
Rounding	Math.round, Math.floor, Math.ceil, Math.trunc
Maximum / minimum	Math.max(a, b), Math.min(a, b)
Absolute value, root	Math.abs(x), Math.sqrt(x)
Random	Math.random() — from 0 to 1
Digits after the point	x.toFixed(2) → a string
Comparison	> < >= <= === !==