Look at it this way. Using number decimals to determine the mathematical number of 1/3, where does it end? It doesn't, it goes on to infinity. 1/3 cannot be determined "exactly" numerically.
That's a nice example, even a 5th grader like me understands!!
Time, degrees, geographics, and as someone points out, illumination... how far down the rabbit hole does it go. I'll continue to disagree... the exact time/place/degrees is repeatable.