A 22m rod with a 7m notch is perfectly ok. You'd then be encoding 7/22. As others have pointed out, the rod could span the known universe and it would still not matter.
Say you found a great message in the representation of 1/7. Weird, since it is a rational so if its representation is infinite, its periodic (you can't write down 1/π or 1/e for example, as these are irrationals.)
Excited you found that message, you want to put your notch exactly at 1/7 on the rod to celebrate it.
But you can't. Your desired notch position will fall between two possible notches, spaced one planck distance apart, and you'll have to pick one of the two.
And when you do, you truncate your message to 15 bytes worth of information.
Say you found a great message in the representation of 1/7. Weird, since it is a rational so if its representation is infinite, its periodic (you can't write down 1/π or 1/e for example, as these are irrationals.)
Excited you found that message, you want to put your notch exactly at 1/7 on the rod to celebrate it.
But you can't. Your desired notch position will fall between two possible notches, spaced one planck distance apart, and you'll have to pick one of the two.
And when you do, you truncate your message to 15 bytes worth of information.