That you cannot represent 1/3 as a non-periodic decimal number is a problem of base 10.
That you cannot represent 1/10 as a non-periodic binary number is a problem of base 2.
These are just mathematic facts. Maybe you don't like the world "problem", but it does not change that this is where we are.
The problem that you cannot represent 0.1 in base 2 FP, is a problem of base 2. You can represent it exactly in base 10 FP.
That you cannot represent 1/3 as a non-periodic decimal number is a problem of base 10.
That you cannot represent 1/10 as a non-periodic binary number is a problem of base 2.
These are just mathematic facts. Maybe you don't like the world "problem", but it does not change that this is where we are.
The problem that you cannot represent 0.1 in base 2 FP, is a problem of base 2. You can represent it exactly in base 10 FP.