Apparently inconsistent arithmetic calculation

(second attempt)
I'm just a beginner at perl. Currently I'm comparing how integers are
supported in several different programming languages:
<http://www.rawbw.com/~rem/HelloPlus/CookBook/CookTop.html#int>
I wrote a test program in perl, but it gives inconsistent results.
Here's the program source:

#!/usr/bin/perl
$a = 'Hello';
$b = 'world.';
$all = "$a $b";
print "$all\n"; # Print a message
$n = 987654321;
print "n = $n\n";
$k = 10000000000000000000000000000000000000000000000000 00000000000000000000;
$n = $n * $k;
print "n = $n\n";
$k = $k * $k;
$n = $n * $k;
print "n = $n\n";
$n1 = $n * $k;
print "n1 = $n1\n";
$k = 10000000000000000000000000000000000000000000000000 00000000000000000000;
$n1 = $n * $k;
print "n1 = $n1\n";

and here's the program output:

Hello world.
n = 987654321
n = 9.87654321e+77
n = 9.87654321e+215
n1 = Inf
n1 = 9.87654321e+284

Notice the two printings of n1. The first time I multiply the value
of n times the value of k that I've been using all along, and the
result is infinity. The second time, I re-assign the value of k to
identical value as it had before, and do the same multiplication as
before, but now the result isn't infinity. What's going on??? This
doesn't make sense to me.

If it makes any difference:
perl -v
This is perl, v5.8.0 built for i386-freebsd

robert maas, see http://tinyurl.com/uh3t wrote:No, you were not using the same value of k all along.
It's obvious if you print out the value of k along with n1.
The first n1 is based on k**2 (1e+138).
The second n1 is based on k (1e+69).

-Joe

From: Joe Smith <j...@inwap.com>Oops. Thanks for pointing that out. Now back to experimentation...
new program source, being more careful:

$a = 'Hello';
$b = 'world.';
$all = "$a $b";
print "$all\n"; # Print a message
$n = 987654321;
print "n = $n\n";
$k1 = 10000000000000000000000000000000000000000000000000 00000000000000000000;
$n = $n * $k1;
print "n = $n\n";
$k2 = $k1 * $k1;
$n = $n * $k2;
print "n = $n\n";
$n2 = $n * $k2;
print "n2 = $n2\n";
$n1 = $n * $k1;
print "n1 = $n1\n";
$k3 = 100000000000000000000000;
$n3 = $n1 * $k3;
print "n3 = $n3\n";
$k4 = 1000000000000000000000000;
$n4 = $n1 * $k4;
print "n4 = $n4\n";
$n4 = $n3 * 10;
print "n4 = $n4\n";

New output, looks fine, thanks!

n = 987654321
n = 9.87654321e+77
n = 9.87654321e+215
n2 = Inf
n1 = 9.87654321e+284
n3 = 9.87654321e+307
n4 = Inf
n4 = Inf