how do 83/100 simplify to 5/6

Answer 1

It doesn't. 100 is not divisible by 6, nor is 83 divisible by 5.

Answer 2

5/6 = .8333333333 .....
83/100 = .8300000000000......

so
5/6 is a little bigger than 83/100
and they are only the same to two significant figures.