Explain whether or not my results 9.876m/s^2 verify that g=9.8m/s^2

Answer 1

The short answer is no.

You would need to perform an error analysis. Since you are quoting so many significant figues, one would expect your measurement was made with better tnan 0.1% accuracay, which would imply that 9.8 m/s^2 is not the correct value.

What is more likely is that there was a systematic error in your measurement, and that you are quoting too many significant figures.

The actual value of g, at the surface of the earth, should be between 9.78 an 9.81 m/s^2. It varies with location, being lowest at the equator.