Why in Python 0.03 % 0.01 = 0.009999999999998 and not 0?

Question

>>> 0.03 % 0.01
0.009999999999999998

Why gives this result, the rest of the division being 0?

And also, instead of 3, give:

>>> 0.03 // 0.01
2.0

Answer 1

Exactly for the same reason that 0.1 + 0.7 is 0.7999999999999 and not 0.8.

• Inaccurate result in broken numbers calculation
• Calculation of incorrect multiplication
• Integer conversation in the rounding account 0.1

Which, briefly, boils down to the summary: IEEE 754.

To get around the problem, you need to use the module decimal:

from decimal import Decimal

a = Decimal('0.03')
b = Decimal('0.01')

print(a % b)  # 0.00
print(a // b)  # 3

Answer 2

Short answer: Precision problems in floating point operations.

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Decimal numbers are represented on the computer as decimal fractions. For example, 0.125(10) = 0.001(2). Nothing new - but if so, take a look at this short summary in Wikipedia on floating comma.

The problem is when we enter numbers that cannot be easily described by a binary fraction that result in infinite tithes like the case of 1/3 = 0.33(3) in the decimal system.

Computers do not have an infinite number of bits so they use approximate representations of the numbers they intend to represent. They are very close presentations but they are still not the number in question.

>>> 0.1
0.1000000000000000055511151231257827021181583404541015625

Python (among other languages) can detect these cases and present the user with a "rounded" representation of the user that corresponds to what would be expected:

>>> 1 / 10
0.1

However this does not change the value that is in memory. So, when doing 0.03 % 0.01 is not even to do the rest of the 0.03 by 0.01 division but rather the rest of the 0.03 by 0.01 memory division, resulting in the error you see:

>>> 0.03 % 0.01
0.009999999999999998

Source: The Python Tutorial - Floating-point arithmetic operations: problems and limitations (in English)