As $val = @values assigns the number of elements in the array to $val, your output confirms my suspicion, i.e. that the lines aren't tab separated, so you get only one value in @values (the entire line) from the split.
Try splitting on whitespace:
#!/usr/bin/perl
use strict;
use warnings;
print " Enter the dilution factor. \n";
chomp (my $df = <STDIN>);
open FILE, "45well.txt" or die $!;
while (<FILE>){
chomp;
my @values = split ' ';
foreach my $val (@values){
my $DNA_conc = $val * $df * 50 ;
print "$DNA_conc\n";
}
}
close (FILE);
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