Why don't elements in the periodic table have whole numbers?

Why would Hydrogen be 1.0079 or gold be 196.96657? The reason for that is because the mass number that you would find on the Periodic Table of Elements is a sort of average of the different isotopes. Hydrogen for example we know has three isotopes: deuterium, protium, and tritium. These would have different masses and they would occur at different frequencies. So, for the sake of argument, you might find one of those isotopes has a 70% occurrence, or in other words, out of the hydrogen found in nature, 70% would be of that isotope. Then maybe another would be 25% and the third would be 5%. So the mass number from the Periodic Table would take into account the frequency of each isotope and its associated mass and determine an average for it. That is why the mass number on the chart could come out to a number down to the ten thousandths place.

They do. The element number is a whole number - a placing in the table based on the number of protons in the nucleus https://en.wikipedia.org/wiki/Atomic_number. The atomic mass is the total protons + neutrons, which varies for different isotopes. (An element is defined by the number of protons, but there can be different numbers of neutrons. This doesn't affect chemical reactions, but can make a lot of difference when it comes to radioactivity and things going bang...) The atomic weight, as TF22 says, is what an average sample would weigh in at if you counted the atoms, weighed them, and then divided the total by the number of atoms. That's not how they do it, but it gives an idea of what you get. So, there's three things we have here: Atomic number (place in table = number of protons) - always a whole number because you can't have half a proton); atomic mass (which isn't a whole number always, as neutrons are just a wee bit heavier than protons; and atomic weight, which is almost never a whole number.