While true, there will be rational numbers you can't represent as floating-point numbers no matter which base you choose. And the moment you start calculating w

While true, there will be rational numbers you can't represent as floating-point numbers no matter which base you choose. And the moment you start calculating with inexactly represented numbers, there is a risk that the errors might multiply and the result of your computation will be incredibly wrong. This is the much bigger "problem" of floats, not the fact that 0.3 is not "technically" 0.3, but off by some minuscule number.