How can I challenge a professor who is ignoring me in an online course? This summer I am taking an online course due to being part of an internship 1000 miles from home. That said, the physics course I am taking the instructor is not grading the tests right. When asked what the right answers are, she responds but then when I ask about the specifics of why I missed them she ignores me.

For example this question,

"An elevator weighing 20 200 N is supported by a steel cable. What is the tension in the cable when the elevator is being accelerated upward at a rate of 3.00 m/s2? (g = 9.80 m/s2)"

She responded that the answer is T = 26383.7 N, then gave me zero points when I wrote 26400 N which seems more correct given significant figures. 

However when I asked about it, she ignored me. 

Because of this kind of thing my test grade went from a 100 to a C-. 

What else can I do?
I would be polite but persistent. 

It may be the case that the online test system auto-grades answers. The instructor may have to go into the system to regrade your answers, and this may be causing the delay in the instructor's response. So, make sure your email contains all the needed information to understand what you answered and why, as well as the extent to which this affected your grade (X answers were marked as wrong for the the same reason). And try to be a bit patient before emailing again (a couple of days).

Is there a discussion of significant digits in your text? Often intro texts have something like this in an early chapter or an appendix. If so, you can point out that part of the book and say that is why you thought rounding to three significant digits was correct. 

In your communication, I would avoid saying you think your answer is better than that of your professor. I would instead try to emphasize that the book led you to believe that your answer was also correct.