I feel that my professor didn't notice a mistake I made on an assignment. Should I have informed the professor of my mistake? This morning, I took my third math quiz of the semester. On the last question, I had solved the presented problem but had not written out the answer according to the directions before time was called, so I simply circled the answer that I did have.

Later this afternoon, I got a notice on my phone that my grade on the quiz had been posted. As it turns out, I got 100% exactly. So, I sent a message to the professor pointing out my mistake.   

Should I have done that?
Whenever I've taught, I would find no problem an action like yours.  You might have pointed out a mistake (in which case it's honest and respectable to point it out), and you might have benefited from partial credit (in which case, it's easy for the professor to tell you or to ignore the correction).

I personally would have also found it a delightful breath of fresh air and a break from the students grubbing and grinding for a few extra points, and would feel warm and fuzzy feelings toward such a student.  Anybody who teaches ends up with a distorted view of the student population because most of their time is spend dealing with the most problematic and annoying students, while the vast majority of the student body who are having no problems are entirely invisible to them.  A reminder of the honesty and integrity of the mostly silent many may thus be quite appreciated.