ANSWER:
Most of the elements have fractional atomic masses.
This is because most elements have isotopes, each with different natural abundance. The atomic mass is actually the average of all the isotopic masses, proportional to their relative abundance. So, their masses have fractional values. Even the monoisotopic elements have atomic masses in fractions. This is due to the mass defect phenomenon that results in some decrease in the mass of nucleus during fusion of nucleons.
(Ref. An Insight Into Objective Chemsitry-11, Ch-01, Q. No. 27)