Abstract: The present paper is a continuation of an earlier work by the author. We propose some new definitions of $p$-adic continued fractions. At the end of the paper we give numerical examples illustrating these definitions. It turns out that for every $m,$ $1<m<5000,\ 5\nmid m$ if $\sqrt {m}\in \mathbb {Q} _{5}\setminus \mathbb {Q},$ then $\sqrt {m}$ has a periodic continued fraction expansion. The same is not true in $\mathbb {Q}_{p}$ for some larger values of $p.$