The problem is that the rounding can give you the same number for two different "large" numbers, so you can't always retrieve the original number from a short one. If you don't care about losing the original number, you can use a hash:

use strict;
use warnings;

my @nums = qw(
    0.0989999999999
    0.0981111111111
    0.6799999999999 
    0.0859999999999
    0.0239999999999
    0.0239999999993
);

my @found = qw(
    0.099
    0.086
    0.024
);

# create a hash, with the rounded number as the key, and
# the original number as the value
# Note that it only store a single value, so only the last
# original number is stored.
my %short_nums = map { sprintf("%.3f", $_) => $_ } @nums;

foreach my $short (@found) {
    if(exists $short_nums{$short}) {
        print "Long num for $short = ", $short_nums{$short}, "\n";
    } else {
        print "No matching long num for $short ...\n";
    }
}
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output:

Long num for 0.099 = 0.0989999999999
Long num for 0.086 = 0.0859999999999
Long num for 0.024 = 0.0239999999993
[download]

... and if you do care about the lose of the original number, then there is no solution :)