Question

Convert 3 over 11 to a decimal by long division

Answer 1

It doesn't matter HOW you do the division.  You can use a calculator,
long division, mental math, short division, a slide rule, a Curta, or an
abacus.  Every possible method must deliver the same answer.  If it
doesn't, then either you made a mistake using it, or else the method
itself doesn't work.

So I'm not going to tell you what method I'm using.

The decimal equivalent of 3 divided by 11 is

                                0.2727272727... .

In order to be exactly equal to 3/11, the '27's must keep going forever,
and never end.    

If you don't have enough time or space on the paper to write an infinite
string of '27's, then you can write some of them and then stop.  The more '27's
you write, the closer your decimal will be to 3/11 , so you can get it as close
as you want.  But if you ever stop, then it won't be exactly equal to 3/11 .