Why does 0.1 + 0.2 != 0.3 in Python, and when do you use Decimal or Fraction?

Q: Why does 0.1 + 0.2 != 0.3 in Python, and when do you use Decimal or Fraction?

**Target Audience:** Python developers who have been surprised by a float result and want to know exactly why, and which numeric type to use instead **Difficulty:** Medium **Python version:** Checked on CPython 3.11 (and in this page on Pyodide 0.25.1, which is CPython 3.11.3) > **How to read this doc:** Each idea is explained in plain language first, then tagged with `📌 Interview term:` so you also learn the exact word an interviewer expects. Every output block in the **Verified** section was copied from a real run of the examples on this page. ## 1. Why This Even Matters — A Story First Try writing one third as a decimal on paper: `0.3333...`. However many 3s you write, you have to stop somewhere, and the number on the paper is a tiny bit less than a third. Add three of your rounded thirds and you get `0.9999`, not `1`. Nothing is broken; you simply cannot write 1/3 exactly with a finite number of decimal digits. A computer has the same problem, but it counts in **base 2** inste

The problem

Question presented to candidate: "If I type 0.1 + 0.2 == 0.3 into Python I get False. Why does that happen, how should I compare floats, and when would you reach for decimal.Decimal or fractions.Fraction instead of float?"

What a strong answer should cover:

A Python float is a 64-bit IEEE 754 binary double (53 bits of precision, sys.float_info.mant_dig == 53); 0.1, 0.2 and 0.3 have no exact binary form, so each literal is stored as the nearest binary fraction and the sum lands on a different neighbour than 0.3
repr() prints the shortest string that round-trips, which is why 0.1 looks exact but Decimal(0.1) or (0.1).as_integer_ratio() reveals the real stored value
Compare with a tolerance (math.isclose, with abs_tol near zero), sum with math.fsum, and know that round() uses round-half-to-even on the stored binary value (round(2.675, 2) is 2.67)
Decimal does base-10 arithmetic with a configurable context (28 significant digits by default, explicit rounding modes, quantize for cents): the right tool for money, and it must be built from strings or ints, not floats
Fraction stores an exact numerator/denominator pair: exact for rational maths, but slower and its denominators can grow without bound
Trade-offs: float is hardware-fast and right for science and measurement; Decimal and Fraction refuse or downgrade when mixed with floats

Code / implementation expected: Optional — show the stored value of 0.1, a tolerant comparison, and a money calculation with Decimal and quantize.

float
decimal
numbers

Try it yourself

Sketch your approach before you read the solution. That is what the interview tests.

Stuck? Get a hint.

A short nudge toward the approach. It will not give the answer away.

Solution

Target Audience: Python developers who have been surprised by a float result and want to know exactly why, and which numeric type to use instead Difficulty: Medium Python version: Checked on CPython 3.11 (and in this page on Pyodide 0.25.1, which is CPython 3.11.3)

How to read this doc: Each idea is explained in plain language first, then tagged with 📌 Interview term: so you also learn the exact word an interviewer expects. Every output block in the Verified section was copied from a real run of the examples on this page.

1. Why This Even Matters — A Story First

Try writing one third as a decimal on paper: 0.3333.... However many 3s you write, you have to stop somewhere, and the number on the paper is a tiny bit less than a third. Add three of your rounded thirds and you get 0.9999, not 1. Nothing is broken; you simply cannot write 1/3 exactly with a

The solution is hidden so you can try first

12 min read · 11 sections

Run the code

Edit the code and run it here. Each console line with an expected value becomes a test.

PythonWhat a float really stores: repr, exact value, isclose, fsum and round

Practice

PythonDecimal for money (quantize, context, rounding) and Fraction for exact ratios