The only thing this proves is that the fraction-to-decimal conversion is inaccurate.

No number is getting converted, it’s the same number in both cases but written in a different representation. 4 is also the same number as IV, no conversion going on it’s still the natural number elsewhere written S(S(S(S(Z)))). Also decimal representation isn’t inaccurate, it just happens to have multiple valid representations for the same number.

A number which is not 1 is not equal to 1.

Good then that 0.999… and 1 are not numbers, but representations.