tmaly has received some excellent advice above and as I understand your contribution, it is an extension of that wisdom. For clarity, for future Seekers, however, to make its relevance explicit (and ramble a bit):

The essential point (IMO, YMMV) in most of the earlier replies is:

Don't treat the phone number as a number!

Granted, it's not clear how tmaly is getting the phone number as a number to begin with, and your sprintf("%d\n",$num); should help, if he has no control over the initial acquisition (if, for example, he's dragging the phone numbers out of a db where the DBA tried to save a few chars by omitting the usual phone number formatting, such as parens around an area code, or dashs or dots to separate the groups).

But, if he can avoid ever having the phone number treated as a number, he can avoid myriad issues:

use strict;
use warnings;

my $string = '99999999999999999999999999';
my $string2 = '9-999-999-999-999-999-999-999-9999'; # see Note 1 below

if ( $string =~ /^(\d)(\1|-)+$/ ) {
   print "\$string might be a phone number: $string \n";
} else {
   print "$string is NOK \n";
}

if ( $string2 =~ /^(\d)(\1|-)+$/ ) {
   print "\$string2 might be a phone number: $string2 \n";
} else {
   print "$string2 is NOK \n";
}

print "stiller's snippet: \n";

my $num = 999999999;
print sprintf("%f\n",$num);
print sprintf("%d\n",$num);
[download]

Note the NON-interpolating quoting of the strings; also added alternation on "-" as this is one of the common formatting schemes mentioned above (and is used in $string2. Output looks like this:

$string might be a phone number: 99999999999999999999999999       # se
+e Note 2
$string2 might be a phone number: 9-999-999-999-999-999-999-999-9999 #
+ also see Note 2
stiller's snippet:
999999999.000000  # a float, as stiller noted, this address's OP's pro
+blem,
999999999         # whereas, Perl makes it easy to use this as a strin
+g
[download]

¹ Interpolating string 2 treats the string as a number and the dashes as subtraction operators
² A 26 digit phone number? Isn't this rather longer than one might expect, even allowing for international access codes and an implicit extension? It is in North American useage, but YMMV elsewhere.

>The essential point (IMO, YMMV) in most of the earlier replies is:
> Don't treat the phone number as a number!

That is a very good point, and you are driving it home I hope.

I should have said that my point was to show that he (at least in this regard) partially introduced the problem himself by formatting the phone number as a float in an attempt to solve his problem, probably only when trying to investigate some odd behavior?

I did ponder though, on the train home, how the problem ever surfaced, just like you do. In your first string you have forced the number to be a string, putting it in quotes. Removing the quotes though, still yields the same output.

It would be very interesting if OP posted a simple program to demonstrate what he actually sees.
regards