What is the purpose of writing electron configuration vs just using the number of electrons off of the periodic table. I know it can be used to determine the number of electrons in each energy level, and therefore, the number of valence electrons. Is there anything else? The number of valence electrons can be found from the periodic table, so why go through that process?
Well, it's almost always this way.
If you know the atomic electronic configuration, you know how many electrons an element has.
If you know how many electrons it has, you'll know how many it needs to have a stable configuration (usually octet).
If you know how many it electrons it needs, you'll know how it reacts with other species.
If you know how substances react, you can predict the reactions involving this substance.
If you know reactions involving this substance, you can either discover a new reaction (knowledge of new reactions makes synthesis easier) or you could invent an unknown compound with interesting properties, which may have its own special uses.