This solution uses some moderately-advanced techniques, but I recommend you study the solution and
perldoc what you don't understand. You will learn some really useful techniques!
#!/usr/bin/perl
use strict;
use warnings;
use Carp;
use Data::Dumper::Simple;
my @array = qw( 7742.8858
7748.5855
5581.2272
1248.2257
6589.5586
5680.1886
8762.1898
5581.2272
5535.5795
6896.6571
6573.2575
6589.5586
5680.1886
5487.3275
5489.5633
6589.5586
5680.1886
);
my %unique = map { $_ => '' } @array;
my @sorted_unique = sort { $a <=> $b } keys %unique;
print Dumper(%unique,@sorted_unique);
---
It's all fine and dandy until someone has to look at the code.