In reality, floats represent exact values on the real number line, and the result of a floating operation is the nearest machine number to the value that would have resulted had the operation been performed to infinite precision if one exists, and a value systematically chosen with zero bias if the exact value lies halfway between two machine numbers.
And BTW, in most financial calculations you don't want to perform operations to infinite precision.
What you want is to have predictable results that do not depend on the environment used to compile and/or run the application.