Well, you are testing in each iteration whether $guess is defined. But that's not necessary. You know that $guess is undefined the first time around, and then never again.

Also, people have suggested that you turn on warnings, but they fail to mention that you should do some checking of $guess (to see whether it's a number) before comparing it to $secret_number - otherwise, you will get warnings.

#!/usr/bin/perl

use strict;
use warnings;

my $secret = 1 + int rand 100;

while (print "Your guess > ") {
    local $_ = <>;
    chomp;

    if (!/\S/ || /quit/i || /exit/i) {
        print "Too bad, you gave up.\n";
        exit;
    }

    if (/\D/) {
        print "You didn't enter a non-negative integer\n";
        next;
    }

    if ($_ == $secret) {
        print "You guessed the number correctly.\n";
        exit;
    }

    my $answer = $_ < $secret ? "less" : "greater";

    print "The number you entered is $answer than the secret number\n"
+;
}

__END__
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That's how I would do it.

Abigail