#!/usr/bin/perl

my @vals;
{
    # set up some high-precision fractions
    use constant PREC => 89;
    use bignum p => -(PREC);
    for my $num (2, 3, 6, 7, 14, 17, 23, 29,
                 47, 48, 49, 196, 197, 224, 467) {
        my $s = 1/$num;
        $s =~ s/0+$/0/;
        $s = substr($s, 0, PREC);
        push @vals, ["1/$num", $s];
    }
}
while (<DATA>) {
    # add some non-numeric stuff, just as demo 
    chomp;
    push @vals, ["", $_];
}

for my $e (@vals) {
    my ($frac, $s) = @$e;
    my $ls = length $s;
    my $ss = $s;
    my $lmin = $ls;
    my $i = 0;
    my $n = 0;
    my $c = 0;
    while ($c++ < $ls) {
        last if $c > $lmin-$n;
        $ss = substr "\x01$ss",0,$ls;
        my $xor = $s ^ $ss;
        $xor =~ s/\0+$//;
        my $l = length $xor;
        if ($l < $lmin) {
            $lmin = $l;
            next if $l+$c > $ls;
            $i = $l-$c; $i = 0 if $i<0;
            $n = $c;
        }
    }
    printf "%-5s : %s", $frac, $s;
    printf "\n     => %s%s", " "x$i, substr $s, $i, $n if $n;
    print "\n";
}

__DATA__
also works with arbitrary strings:
thisisjustblahblahblahb
yadda, yadda, yadd