Why does a loop summing 0.04 in Java result in unexpected rounding errors?

Floating-Point Rounding Errors in Java

In a Java program, a loop summing the value 0.04 to itself 25 times yields unexpected results between the 6th and 10th iterations. Instead of incrementing by 0.04 as expected, the sum round to incorrect values like 0.24000000000000002 and 0.39999999999999997.

This strange behavior is due to the nature of floating-point arithmetic. Floating-point values are represented using binary floating-point format, which cannot exactly represent many decimal fractions. Instead, they store values as sums of negative powers of two.

For instance, 0.5 can be exactly represented as 2^-1, and 0.125 as 2^-3. However, the decimal value 0.96 cannot be precisely represented as a sum of negative powers of two, resulting in a slight rounding error when stored in a floating-point variable.

When performing arithmetic operations on floating-point values, these rounding errors can accumulate, causing the sum to deviate from the expected value. This is why the sum of 25 iterations of 0.04 does not remain an exact integer multiple of 0.04.

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