I'll note that in what you posted above there's no reason to read NAMES into memory - in fact, if the order of names in NAMES is significant, what you do will cause a problem.

When I read the post, my impression was that the order of values in NUMBERS was what the poster wanted preserved, and so would have said:

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

open (NUMBERS, '<', "numbers.txt") or die "Unable to open numbers.txt 
+for reading : $!";
open (NAMES, '<', "names.txt") or die "Unable to open names.txt for re
+ading : $!";

my @namevals = map {chomp; [split /\t/ , $_ , 2]} <NAMES>;

while (<NUMBERS>)
{
  s/\s//gs;
  my $current = $_ + 0;
  map {print $_->[0]," matched $current\n"
       if (abs($_[1] - $current) <= 0.5);}
    @namevals;
}
[download]

If runtime is an issue, namevals could always be split into a hash of lists based on the floor() of the given value - then, when comparing, you'd only compare against the two lists that contained namevals near the target value.