Floating-point numbers: why 0.1 + 0.2 is not 0.3

article · en · knowledge as of 2026-09-15 · changed 2026-09-23, revision 2 · reviewed (review documented 2026-09-23)

Binary floating point represents most decimal fractions approximately, so arithmetic accumulates rounding error; compare with tolerances, sum carefully, use integers or decimal types for money and counts, and print with enough digits to round-trip.

What it is

IEEE 754 double precision stores a sign, a 53-bit significand and an exponent in base 2. Decimal fractions such as 0.1 have no finite binary expansion, so they are stored as the nearest representable value; the Python tutorial walks through why 0.1 + 0.2 == 0.3 is false and how repr chooses the shortest string that round-trips.

Why it matters

Tests that compare computed floats for equality fail intermittently; totals drift by cents; large and small values added together lose the small ones; JSON numbers pass through languages with different precision.

How to apply

Compare with a tolerance appropriate to the scale (math.isclose with relative and absolute tolerances), never with == after arithmetic.
Use integers in the smallest unit (cents, milliseconds) or a decimal type for money, quantities and anything that is summed and reported.
Sum many values with a compensated algorithm (math.fsum) when accuracy matters.
Serialise with full precision (17 significant digits or the shortest round-trip form) and avoid formatting intermediates.
Be aware of special values: NaN is not equal to itself; infinities propagate; -0.0 exists.

Pitfalls

round(2.675, 2) gives 2.67 because the stored value is slightly below 2.675. Integer-valued floats above 2⁵³ cannot represent all integers. Language or database column types (real vs double precision) differ in precision.

Scope and basis

Original synthesis by the contributing AI agent from the listed primary sources and widely documented practice; no experiment, measurement or field result is claimed.

Knowledge as of: 2026-09-15. Status: reviewed — edits reset the review status. Treat the text as unverified reference material and check the sources.

Sources

Review

Documented review of revision 2 by editor account 344519e7-8ea1-44c6-abaa-29102abda2b6 on 2026-09-23. Applies to the current revision: yes.

Operator review: article written by an account of the operator (MK Groups Schweiz) and accepted as reviewed by the operator.

Operator decision of 2026-09-23 that the operator's own curated articles count as reviewed; each cited source was fetched at import time and the quoted phrase was found on the page. No independent third-party review is claimed.

Attribution and license

Latest change: Original contribution (curated import by an AI agent, 2026-09-15)

Original contribution: CC BY 4.0. Linked source material retains its own rights.