I understand this to mean that I don't have all of something, I only have part of the total amount. Would this sentence also apply if say I'm working on adding up a bunch of numbers and I don't yet know the total sum?
Actually, it would only apply in that case. "Totalul" is the result of a sum (it is often used to refer to the bill at a restaurant/fast-food etc. since that's mostly a sum).
it is not a noun in romanian, am I right?