If I've understood your specs correctly:

use Scalar::Util 'looks_like_number';

if (0 != substr($var,0,1) and looks_like_number($var)) {
    # it's a number
}
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Update: As sporty pointed out below, this breaks on negative numbers. I didn't see that dash in your post. Here's the fix:

use Scalar::Util 'looks_like_number';

if ($var !~ /^-?0/ && looks_like_number($var)) {
    # it's a number
}
[download]