JS Numbers

JavaScript Numbers: Floating-Point Standard (IEEE 754) & Precision

In JavaScript, all numbers are double-precision 64-bit binary format IEEE 754 floating-point numbers. JavaScript does not distinguish between integers and floats at the primitive type level.

Number Bit Layout (64-Bit IEEE 754)

flowchart LR
    BitLayout["64-Bit Float Layout"] --> Sign["1 Bit: Sign (+/-)"]
    BitLayout --> Exponent["11 Bits: Exponent"]
    BitLayout --> Mantissa["52 Bits: Mantissa / Fraction"]

Precision & Limits Summary

Practical Code Example

// Demonstrating JavaScript numeric behavior, limits, and floating point issues

// 1. The Classic Floating Point Precision Issue
const sum = 0.1 + 0.2;
console.log(`0.1 + 0.2 = ${sum}`); // 0.30000000000000004
console.log(`Direct comparison (0.1 + 0.2 === 0.3): ${sum === 0.3}`); // false

// Solution: Epsilon tolerance comparison
const isNearlyEqual = Math.abs((0.1 + 0.2) - 0.3) < Number.EPSILON;
console.log(`Epsilon Comparison Safe Equal: ${isNearlyEqual}`); // true

// 2. Safe Integers vs Overflow
console.log(`Max Safe Integer: ${Number.MAX_SAFE_INTEGER}`);
const unsafeInt = Number.MAX_SAFE_INTEGER + 2;
console.log(`Unsafe int computation: ${unsafeInt}`); // Precision lost!

// 3. Special Numeric Values: NaN and Infinity
console.log(`1 / 0: ${1 / 0}`);               // Infinity
console.log(`"abc" * 5: ${"abc" * 5}`);       // NaN (Not a Number)

// Checking NaN safely
console.log(`Number.isNaN("abc" * 5): ${Number.isNaN("abc" * 5)}`); // true

Best Practices & Gotchas

• Use Number.isNaN() Instead of isNaN(): isNaN("abc") coerces "abc" to a number first, returning true. Number.isNaN("abc") checks strictly without coercion.
• Format Currency with toFixed(2) or Intl.NumberFormat: Never calculate money directly using float additions without rounding or cents conversion.
• Use BigInt for Large Integers: For integers larger than $2^{53} - 1$, use BigInt.

Self-Check Challenge

Explain why NaN === NaN evaluates to false in JavaScript, and how to properly check if a variable is NaN.