Rings, when relaxed, are not circular because of the gap. If they were they would create an unequal radial pressure when fitted into the bore. They are in fact manufactured to take on a form, when relaxed, rather like that of a halved apple, they become circular when fitted into the correct bore and thereby exert an equal radial pressure all around the whole circumference.
So bore a series of accurate holes in some pieces of sheet, (about the same as the axial thickness of the rings for convenience), starting with the nominal bore and going up in 0.010” steps. With a ring inserted and held up to a good light a ring of the wrong size will quickly show up an uneven fit.