I don't think you can see them as a range. Sure, you can think of the float representation of 0.1 and 0.2 as a small range around those values, but what does th

I don't think you can see them as a range. Sure, you can think of the float representation of 0.1 and 0.2 as a small range around those values, but what does that make 0.1 + 0.2, or 0.1 * 0.2, or 0.1 ** 0.2? Now the resulting float no longer represents the range of potential conversion error. And at the same time, integer values (up until some decently high numbers) are represented correctly, so they would need a different range.