Atomic numbers and atomic mass numbers are whole numbers because they are based on the fundamental properties of atoms.
The atomic number represents the number of protons in the nucleus of an atom. Protons are subatomic particles with a positive charge, and they determine the identity of an element. Since the concept of atomic number is based on counting the number of protons, which are indivisible particles, it is always a whole number.
The atomic mass number represents the total number of protons and neutrons in the nucleus of an atom. Neutrons are also subatomic particles, but they have no electrical charge. The mass of both protons and neutrons is approximately equal to 1 atomic mass unit (amu). Since atomic mass number is a sum of whole numbers (protons + neutrons), it is also always a whole number.
It is important to note that the atomic mass listed on the periodic table is often a decimal number because it represents the weighted average of the masses of all the naturally occurring isotopes of an element. Isotopes are atoms of the same element with different numbers of neutrons, which slightly affects their atomic masses. However, the atomic mass number for a specific isotope will still be a whole number because it only considers the sum of protons and neutrons in that particular isotope.