As one might expect, this is already answered in the FAQ:

How do I determine whether a scalar is a number/whole/integer/float?

Assuming that you don't care about IEEE notations like "NaN" or "Infinity", you probably just want to use a regular expression.

   ...
   if (/^-?\d+$/)       { print "is an integer\n" }
   if (/^[+-]?\d+$/)    { print "is a +/- integer\n" }
   ...
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