111.009 mm
It has :
6 significant figures.
As the zero to the left of 9 is less than 5.
So we have to get rid of it , and it is cancelled and 9 with it also get cancelled.
So, it will become,
111.0 mm
It has 4 significant figures:
*3 nonzero digits
*1 trailing zero
So according to above explanation,
b. 111.0 mm, is the correct answer.