That's an interesting point I had not considered. My view (mostly from the math side, my shallow dive into physical systems was just from a PDE class in grad school) is from the view of unstable differential equations where very small changes to initial conditions can cause massive changes to the output of the system. My uninformed instincts would tell me that even with orders of more digits than atoms in a physical system, changes smaller than the available accuracy to initial conditions could have significant impact on the eventual state of the system.