Maybe the file isn't tab delimited, as you think it is. In this case, the split wouldn't work, and $val (in the multiplication) would be entire line...

To debug such issues yourself, just print out the value(s) in question, in this case $val.

Also, the line $val = @values; doesn't make any sense here — it's superfluous.

open FILE, "96well2.txt" or die $!;
 while (<FILE>){
 chomp $_;
  @values = split('\t', $_);
  $val = @values;
  print $val;
 }
 close (FILE);
[download]

This is what printing $val gives 111111111111

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);
[download]

use warnings;
print " Enter the dilution factor. \n";
 chomp ($df = <STDIN>);
 open FILE, "45well.txt" or die $!;
 while (<FILE>){
 chomp $_;
  @values = split('\t', $_);
  $val = @values;
  foreach $val (@values){
print "df >>>$df<<<\n";
print "val >>>$val<<<\n";
 $DNA_conc = $val * $df * 50 ;
 print $DNA_conc;
 print"\n";
 }
 }
 close (FILE);
[download]

That's Tip #2 from the Basic debugging checklist.

$df = is the user input value. so if i enter 10 $df = 10. $ val is giving the output as 111111. so something is wrong here. the file looks like this

0.250   0.413   0.432   0.345   0.786   1.001   0.987 
0.984   0.125   0.678   0.243   0.657   0.342   0.743   
0.986   0.734   0.764   0.650   0.457   0.965   0.836
[download]

When I copied your data, I get single spaces instead of tab characters. Try to use split as follows:

use strict;
use warnings;

my $df = 10;
while (<DATA>) {
    chomp $_;
    my @values = split;
    foreach my $val (@values) {
        my $DNA_conc = $val * $df * 50;
        print $DNA_conc;
        print "\n";
    }
}

__DATA__
0.250   0.413   0.432   0.345   0.786   1.001   0.987 
0.984   0.125   0.678   0.243   0.657   0.342   0.743   
0.986   0.734   0.764   0.650   0.457   0.965   0.836
[download]

This is the output I get:

125
206.5
216
172.5
393
500.5
493.5
492
62.5
339
121.5
328.5
171
371.5
493
367
382
325
228.5
482.5
418
[download]