Atomic mass number is simply the sum of the number of protons and neutrons in nucleus of an atom.
The number of protons and neutrons is always a whole number. It will never be fraction, as protons and neutrons are smallest and cannot be broken again.
So, their sum will also, be always whole.
So, atomic mass number is always whole.
Example: Carbon has 6 protons and 6 neutrons. So, its atomic mass number is 6+6=12.