PythonHow-ToBeginner · 3 min read

Why 0.1 plus 0.2 is not equal to 0.3 in Python explained

In Python, 0.1 + 0.2 is not exactly equal to 0.3 because floating-point numbers are stored in binary, which cannot precisely represent some decimal fractions. This causes tiny rounding errors, making the sum slightly different from 0.3.

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Syntax

In Python, you write decimal numbers using float type like 0.1, 0.2, and 0.3. When you add two floats, Python uses binary floating-point arithmetic internally.

0.1, 0.2, 0.3: decimal numbers as floats
+: addition operator
Comparison with == checks if two values are exactly equal

python

a = 0.1
b = 0.2
c = 0.3
print(a + b == c)

Output

False

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Example

This example shows that adding 0.1 and 0.2 does not exactly equal 0.3, and prints the actual sum to reveal the tiny difference.

python

a = 0.1
b = 0.2
c = 0.3
print('0.1 + 0.2 == 0.3:', a + b == c)
print('Actual sum:', a + b)

Output

0.1 + 0.2 == 0.3: False Actual sum: 0.30000000000000004

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Common Pitfalls

Many beginners expect 0.1 + 0.2 == 0.3 to be True, but floating-point precision causes this to be False. This can lead to bugs when comparing floats directly.

To avoid this, use a small tolerance to check if two floats are close enough instead of exactly equal.

python

a = 0.1
b = 0.2
c = 0.3
# Wrong way: direct equality
print(a + b == c)  # False

# Right way: check closeness with tolerance
tolerance = 1e-9
print(abs((a + b) - c) < tolerance)  # True

Output

False True

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Quick Reference

Floating-point numbers store decimals approximately in binary.
Direct equality checks can fail due to tiny rounding errors.
Use a tolerance (like 1e-9) to compare floats safely.
Python's math.isclose() function can also help compare floats.

python

import math
print(math.isclose(0.1 + 0.2, 0.3))

Output

True

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Key Takeaways

Floating-point numbers cannot represent some decimals exactly, causing small errors.

Directly comparing floats with == can give unexpected False results.

Use a small tolerance or math.isclose() to compare float values safely.

The sum 0.1 + 0.2 is very close but not exactly 0.3 in Python.

Understanding floating-point precision helps avoid bugs in numeric code.