Why does changing the sum order returns a different result?

Question

Why does changing the sum order returns a different result?

23.53 + 5.88 + 17.64 = 47.05

23.53 + 17.64 + 5.8

Answer 1

Floating point numbers are represented using the IEEE 754 format, which provides a specific size of bits for the mantissa (significand). Unfortunately this gives you a specific number of 'fractional building blocks' to play with, and certain fractional values cannot be represented precisely.

What is happening in your case is that in the second case, the addition is probably running into some precision issue because of the order the additions are evaluated. I haven't calculated the values, but it could be for example that 23.53 + 17.64 cannot be precisely represented, while 23.53 + 5.88 can.

Unfortunately it is a known problem that you just have to deal with.