Floating point values are binary scientific notation with a fixed precision. All of the unintuitive behaviour of floats is repeated if you imagine conducting d

Floating point values are binary scientific notation with a fixed precision. All of the unintuitive behaviour of floats is repeated if you imagine conducting decimal calculations yourself in said scientific notation, with intermediate rounding at every step. Floats are only ranges in that each real number (within the overall range limit) has a unique floating point representation to which it is closest, up to rounding at the precise interval boundary. Floats can be extended to interval arithmetic, but doing so requires the extra work of keeping track of interval limits. When calculations lose precision (through cancellation of digits in the floating point representation), the interval of uncertainty is larger than the floating point precision.