s/\G0(?=\d)/ /g;
[download]

$num =~ s/\G0/ /g;
[download]

-- Randal L. Schwartz, Perl hacker

Please take the following with a grain of salt. Ovid has already given the best answer.
It makes me wince, now, but it was actually used in production to strip leading zeros from numbers in a list, in the first real Perl program I ever wrote.

#!/usr/bin/perl -w
@numberarray = qw(00000900011 10001000100 00022200101); 

for $digits (@numberarray){ 
    @temparray = split (//,$digits); 
    $incr=0; 

        while ($temparray[0] eq 0) {
           shift @temparray; $incr++;
        } 
        unshift (@temparray," "x$incr); 
        $digits = join('',@temparray);
        print "$digits\n";
}
[download]

I couldn't discover a better way than to shift out the zeroes and unshift the replacing text, then join the result together.
It isn't pretty, but, as far as I can tell, it doesn't break.

mkmcconn
novice

Update:
And now, a monk, I never would have posted this (wonderful what a few weeks at perlmonks can do), but if I had, I would have suggested to novice mkmcconn that even taken with a grain of salt, numerous difficulties in his solution could be avoided by writing it this way:

#!/usr/bin/perl -wl
use strict;
my @numberarray    = qw(000000 000002 001110 010201 010010 001000 0001
+20 010030); 

for (@numberarray){ 
    next if $_    == 0;
    my @array      = split //; 
    my $incr       = 0; 
    
    while ($array[0] eq 0) {
       shift @array;
       $incr++;
    } 
    unshift (@array,"\x20" x $incr); 
    print @array;
}
[download]

It will be interesting to find out what advice I might give myself someday, about this update.
mkmcconn