Question

why do we reach equation 3 expressing 0.29 in the form of p by q and q is not equal to zero

Answer 1

Because you can't divide by zero.
In sufficiently well-behaved algebras (this is certainly true of the rational numbers, but it's more generally true) 0 is an additive identity, so 0 + q = q for all q, and multiplication distributes over addition.
We have p.q = p(q + 0) = p.q + p.0
and p.0 must be the additive identity. We can't have more than one additive identity - exercise for the reader!
So p.0 = 0 for all p. Similarly 0.p = 0 for all p.

Since multiplying by 0 always produces 0, dividing 0 by 0 is ambiguous (it could be anything) and dividing anything else by 0 is not possible. Either way, dividing by 0 is not defined.

I have assumed that p + q = p implies q = 0. It's sufficient that the numbers under consideration form a group under addition, which is true for the rationals, but not necessary (for instance, it's also true for the natural numbers). An operation for which 
p op q = p does not imply p = 0 would hardly count as an "addition".