Both the advice from SankoR and, even more so, the observation by FunkyMonk are clearly on target. In the hope of offering some additional clarity:

printf produces output; sprintf merely formats

However, I'm perplexed by your use of "string" in the phrase "save it as a string" as well as by some other aspects of the question. For example, do you mean that $n and $u are floating point numbers (assumed below) or can they be ints; a mixture; or something else??

All the above leads me to send a question back: Does this come somewhere close to your intent?

#!/usr/bin/perl
use strict;
use warnings;

# 816487

my $n = 3.123;
my $u = 3.678;
my $i= 0;
my (@array, $array);

for (1..10) {
    $n -= ($n * $u) * $u;
    $array[$i] = int(abs($n));
    $i++
}

for (@array) {
    print "$_ \n";
}
[download]

Output, for $n=3.123, $u=3.678

39
490
6140
76922
963664
12072486
151240294
1894690621
23736085384
297358177092
[download]

and for $n=3.123, $u=4.0

46
702
10540
158101
2371528
35572921
533593828
8003907421
120058611328
1800879169921
[download]

And another question: "Waaaay off? Helpful?" (I hope the latter.)