Why Do Python's Floating-Point Numbers Produce Unexpected Rounding Errors?

Python Floating-Point Rounding Errors

Floating-point numbers in Python can lead to unexpected rounding errors. Understanding the limitations of floating-point arithmetic is crucial.

In the provided code, the error stems from the fact that some numbers cannot be represented exactly as floating-point numbers. When converting from an integer to a float and dividing by 100, the resulting number is approximated. In this case, the approximations for 0.29 and 0.58 were closer to 0.28 and 0.57, respectively, resulting in identical file names.

This behavior is not systematic, as it only affects certain numbers that cannot be accurately represented using powers of two. To demonstrate this, the following Python script was created:

Running this script for various values of n shows that the rounding error does not follow a specific pattern.

The root cause of this issue lies in the nature of floating-point arithmetic. For more information, refer to "What Every Computer Scientist Should Know About Floating-Point Arithmetic." This article provides valuable insights into the complexities and limitations of floating-point operations.

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