It can be 2-3 times more precise, but it doesn’t have to be. You could just as easily say the imperial system is 8 times more precise because the 1/64th inch exists. You just chose 1/8th because that’s the amount of precision you wanted, but it could just as easily be 2 mm.

If you use a ruler and round all of your cuts to the nearest 1/8th inch, in practice that’s no different than using that same ruler and rounding all of your cuts to the nearest 2 mm.