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.