The issue is that you are missing the possibility of decimal floating point, which is also defined in IEEE 754 but which is typically not exposed as a primitive

The issue is that you are missing the possibility of decimal floating point, which is also defined in IEEE 754 but which is typically not exposed as a primitive in programming languages. Imagine a BCD mantissa. That can encode 12.3456 exactly. So it's not "since computers use binary", but "since we use binary floating point". There are fair arguments that we made that choice because of efficiency concerns driven by the fact that "computers use binary", but I don't think that really helps the explanation. Note that the original objection was picking at a nit that I am not sure I would have picked at, I am just seeking to clarify.