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.