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test[x_] := With[{a = Length[First@RealDigits[x]], b = Round[Precision[x]]}, a == b ] the test is False for any Integer and Rational, exact symbols like Pi, etc. Its also False for N[m, n] for any m power of 10 and n been an Integer. As well as for some other Real numbers, I'm guessing depending on the internal representation. test[N[1, 10.3]] ...

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