One way out of the problem is to use rational numbers.

#! /usr/local/bin/perl

use strict;
use warnings;
use Math::BigRat;

my $x = Math::BigRat->new;
my $delta = Math::BigRat->new('1/10');

for ($x=1; $x < 2; $x += $delta) {
  print "$x\n";
}

print "Stop: x=$x\n";
print "No, x is not 2.\n" if $x != 2;

__PRODUCES__
1
11/10
6/5
13/10
7/5
3/2
8/5
17/10
9/5
19/10
Stop: x=2
[download]

Oddly, I had to change the less-than-or-equal comparator to less-than. I'm not sure why this is different to your code, but then again I never use C-style for loops, so there may be some subtlety I'm overlooking. I would have written it as follows:

my $x = Math::BigRat->new(1);

while  ($x < 2) {
  $x += $delta;
  print "$x\n";
}
[download]