2 is a number.

No, 2 could be a number or a string base on the context as how you use it. A better answer is to point out what he really misunderstood: the context.

It is pretty straight to simply change == to eq, and quot 2:

use Tk;
use Tk::NoteBook;
use strict;
use warnings;
use strict;
use warnings;

while (my $data = <DATA>) {
chomp $data; 
print $data;
if ($data eq "2"){print "->got 2\n"}
}

print "Enter a 2\n";
my $input = <>;
chomp $input;
if ($input eq "2"){print "->got 2\n"}

__DATA__
1
2
3
4
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