My method is general - not limited to fraction equal to unity, which seems to be your assumption. I showed how to find the fraction equal to any rational number, not greater than unity, that has a repeating decimal, using the repeat length, I'll now call: "L."Hi Billy T. ... I have already mentioned where trivial non-actions (like using 1/1, 9/9 'constructions') as a 'step' in 'proofs' is defeating the purpose of fractional treatment first and foremost without introducing self-serving circuitous constructions which assume a-priori what the 'fraction' will be (because you already have the abstraction of 1/1, 9/9 and unity as somehow being relevant to the FRACTIONAL states being discussed). ....

In post 397, a part of post 301, I applied my procedure to a unity fraction as that is the subject of the thread, but in post 301 I also applied it to the Repeating Decimal RD = 0.123123123123... which has L = 3. In that case my general method for finding the (now called RF, for Rational Fraction) is RF = RD = abc / 999 as L=3 with a=1, b=2 & c =3. Thus by the "green result" of 397 (or 301) We have RF = 123 / 999 = 41 / 333, which certainly is not a unity fraction.

PS I'm not sure I understood your point, if you had one, other than the one I replied too.

Again I note that

**the burden of proof, is extraordinary, and on those trying to tell why my method, FAILS in the special case of L = 1 with a =9**I.e. why 9/9 = 1 is not 0.999... when works in an infinite number of other cases for finding the RF equal to ANY repeating decimal, RD, not greater than unity.