The atomic masses in the Periodic Table are not integral numbers. For example, carbon is listed as 12.011 amu instead of 12.000 amu. Why?

The reason that the atomic masses shown on the periodic table include fractions, is to account for the other isotopes of the element, not just the pure element. Remember, an isotope is a atom of an element with a reduced or increased number of neutrons. This changes the atomic mass but not the charge. The number is calculated by multiplying the atomic mass of each isotope of the element with its percent abundance found in nature. Therefore it is an averaged atomic mass for all of the element. For example, carbon-12 may (I don't know the real numbers) have a % abundance of 98.5%, and carbon-14 may have a percent abundance of 1.5%, so that is why carbon would have an atomic mass greater than 12.000.