Here is my (fixed) simple solution. The output is slightly different in that it puts a "p" before the start of the periode.

#!/usr/bin/perl

use strict;
use warnings;
divide(1,18);
for (my $i=1; $i<20; ++$i) {
    print "1/",$i,"=",divide(1,$i),"\n";
}

sub divide {
    my ($z,$n)= @_;
    my (
        %rec,
        $rem,
        $res,
    );
    my $dig= '';
    $res= int($z/$n);
    $z-= $res*$n;
    while ($z) {
        $z*=10;
        $rem= $z % $n;
        $dig.= int($z/$n);
        if (defined $rec{$rem}) {
            my $p= $rec{$rem};
            if ($p>0 and substr($dig,$p-1,1) eq substr($dig,-1)) {
                substr($dig,-1,1)='';
                --$p;
            }
            return $res. "." . substr($dig,0,$p)."p".substr($dig,$p);
        }
        $rec{$rem}= length($dig);
        $z= $rem;
    }
    return $res . "." . $dig;
}
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output:

1/1=1.
1/2=0.5
1/3=0.p3
1/4=0.25
1/5=0.2
1/6=0.1p6
1/7=0.p142857
1/8=0.125
1/9=0.p1
1/10=0.1
1/11=0.p09
1/12=0.08p3
1/13=0.p076923
1/14=0.0p714285
1/15=0.0p6
1/16=0.0625
1/17=0.p0588235294117647
1/18=0.0p5
1/19=0.p052631578947368421
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