Q:

Does $p/q$ has at most $n-1$ zeros after a non zero number in its decimal expansion

Is the following true?

Let $p$ and $q$ be integers and let $q$ be an integer with $n$ digits, then $p/q$ has at most $n-1$ zeros after a non zero number in its decimal expansion.

A:

The decimal expansion (where wlog. $p>0$) is computed as follows:

Perform division with remainder: $p=a\cdot q+b$ with $0\le b<q$. Write $a$ and a decimal point. 
Let $p\leftarrow b$
[Now $0\le p<q$]. Perform division with remainder: $10p=a\cdot q+b$ with $0\le b<q$. 
[Now $0\le a\le 9$]. Write $a$. If $b=0$, terminate; otherwise goto 2.

If step 4 outputs $k$ consecutive zeroes, then the value of $p$ gets multiplied by $10$ in each round. In the $k$th of these rounds $p$ is $10^{k-1}$ times the value it was in the first such round, and this must be $<q$ (and on the other hand nonzero). Hence $k$ zeroes mean that $q>10^{k-1}$.

