Understanding IEEE‑754 Floating‑Point Precision Issues in JavaScript

When adding numbers like 0.1 + 0.2 in JavaScript, the console prints 0.30000000000000004, which feels counter‑intuitive.

JavaScript’s sole numeric type Number is implemented using the IEEE‑754 double‑precision binary floating‑point format, a standard shared by many programming languages, and therefore inherits its rounding behavior.

IEEE‑754 represents a value as S + E + M = 64 bits, where S is the sign bit, E the 11‑bit exponent (biased by 1023), and M the 52‑bit mantissa; the actual value is (‑1)^S × 1.M × 2^(E‑1023).

Example 1 – Decimal 2.5: Converting 2.5 to binary yields 10.1. After normalizing to 1.01 × 2^1, the sign bit is 0, exponent becomes 1024, and the mantissa fits within 52 bits, so the value is stored exactly without loss.

Example 2 – Decimal 0.1: Binary conversion produces an infinite repeating fraction 0.0001100110011…. After normalizing and rounding to 52 mantissa bits, the stored value corresponds to 0.10000000000000000555, introducing a small error that propagates when performing arithmetic such as 0.1 + 0.2.

The same process applied to 0.2 yields a similar rounding error, and the sum of the two approximated values results in the observed 0.30000000000000004.

Mitigation strategies: Use built‑in methods to control precision, e.g., x.toFixed(2), parseFloat(x.toPrecision(3)), or Math.round(x). For more demanding cases, employ arbitrary‑precision libraries such as bignumber.js, decimal.js, or big.js.

References include “JavaScript: The Good Parts”, articles on floating‑point traps, and the IEEE‑754 specification.