The decimals are also there to show that a standard sample of that element will contain different isotopes in certain standard ratios. For example, there are two isotopes of Cl which are present in nature, with masses (to the nearest whole number) of 35 and 37 in a 3:1 ratio. So, 0.75 x 35 + 0.25 x 37 = 26.25 + 9.25 = 35.5, which is the atomic mass of Cl as listed on periodic tables (to one decimal point).
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