It's not that precision can't be arbitrarily recorded higher in fraction, it's that precision can't be recorded precisely. Decimal is essentially fractional that's written differently and ignoring every fraction that isn't a power of 10.

How can a measurement 3/4 that's precise to 1/4 unit be recorded in decimal using significant figures? The most-correct answer would be 1. "0.8" or "0.75" suggest a precision of 1/10th and 1/100th, respectively, and sig figs are all about eliminating spurious precision.

If you have 2 measurement devices, and one is 5 times more precise than the other, decimal doesn't show it because it can only increase precision by powers of 10.

In the case of 1/64th above, if you just divide it out it shows a false precision of 1/100,000.