When you receive a syntax error on the calculator, it usually indicates that you either made a typographical error or tried to perform an operation in such a way that the calculator does not understand it or does not have an algorithm to use to compute it.
1 divided by 0 is an interesting example though. Even though your syntax was, in fact, correct (you pressed a number key, then the division key, and then another number key), the operation is not possible to compute.
It would actually be more correct for the calculator to give you a "Does not compute" error or something, rather than a syntax error.
As for 99999999+1, there's not really a problem with the syntax there either, it's just that the calculator probably doesn't have enough room to display that many digits on the screen at once.
A real syntax error might be something like this: 100 + + 1
That's an ambiguous expression. Reading that, you're not really sure of how to compute it, and neither is the calculator. I broke syntax there. I broke the rules governing how we represent mathematical expressions.
A real syntax error occurs when you do not express yourself clearly. It's the same in mathematics as it is in language, if that makes a better analogy.