Why is the mass for elements on the periodic table written as a decimal?

A perfectly logical question! The atomic mass of an element is equal to the number of protons plus the number of neutrons constituting its nucleus. Protons and neutrons have the mass of an Hydrogen nucleus. So, to find the atomic mass of any element, we basically sum up integer numbers of Hydrogen nuclei. Where do all those decimals come from?

What complicates this simple picture is that, for most elements, there may exist different sort of nuclei, all with different masses. These are called isotopes, which in Greek means "the same place" because they all occupy the same spot on the periodic table. The one assigned to each proteiform element by Dmitri Mendeleyev when, back in 1865, he counted all these tiny particles up.

If these isotopes are squeezed together in the same Mendeleyevian boxes, it is because they have the same electrical charge, the same number of protons, though not the same number of neutrons.

To give you the simplest example, the Hydrogen's nucleus only has one proton. But there exist in nature two additional isotopes of that element. You have probably heard their names : Deuterium and Tritium. Their charge is still +1, and they still occupy the first box on the element's table. But Deuterium has one neutron in addition to the regular Hydrogen's proton; and the Tritium has two. Hence their different masses.

OK, I can hear you saying, the atomic masses are rispectively 1, 2, and 3. Where do the decimals come from? (by the way, the little “e” rotating about the 3 Hydrogen nuclei of the Wikipedia image is the lonesome electron whose task is to balance the electrical charge).

If someone asked you now what is the average atomic mass of Hydrogen what will you say? A clever answer would be to sum up the three isotopes' masses and divide by three.

Well, that's ##(1+2+3)/3 = 2##.

Why is the atomic mass of Hydrogen equal to 1.00794 ?

Scientists would not be scientists if they didn’t dream up all sort of complications. They did not stop at an arithmetic average. They wanted a more realistic one. So they evaluated the quantities of the three isotopes available on Earth and plugged them into the equation. They established, in other words, a weighted average. There is plenty of Hydrogen in our atmosphere; there is a lot less Deuterium and even less Tritium in the ocean waters (that’s where the world's "heavy water" supplies are to be found).

So, when you throw those factors in, you are no longer adding ##1+2+3##, but a lot of ##1 +## a tiny fraction of ##2## and an itsy bitsy fraction of ##3##. Hence the 1 and the 5 decimals. This was certainly too long. I hope that at least it was clear.