I have a great confusion in significant and rounding off data, 834.8501 I have to be asked to round off to four significant, I have done it as 834.8, but teacher said it would be 834.9, she says rounding of 501 is greater than 500 so one is add into 8. ?

Yes. Round up when the digits you remove are more than half of the next power of #10# like #501/1000#. Round to the even terminal digit when the removed digits are exactly half of a power of #10#.