Change your the print to

printf "%.16e\n", $x;
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and you get

1.0000000000000000e+000
1.1000000000000001e+000
1.2000000000000002e+000
1.3000000000000003e+000
1.4000000000000004e+000
1.5000000000000004e+000
1.6000000000000005e+000
1.7000000000000006e+000
1.8000000000000007e+000
1.9000000000000008e+000
Stop: x=2.0000000000000009e+000
No, x is not 2.
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1/10 is a periodic number in binary, just like 1/3 is a periodic number in decimal.

You'll get better results if you avoid accumulating the error:

for ( 1*10 .. 2*10 ) {
  my $x = $_/10;
  printf "%.16e\n", $x;
}
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1.0000000000000000e+000
1.1000000000000001e+000
1.2000000000000000e+000
1.3000000000000000e+000
1.3999999999999999e+000
1.5000000000000000e+000
1.6000000000000001e+000
1.7000000000000000e+000
1.8000000000000000e+000
1.8999999999999999e+000
2.0000000000000000e+000
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Basically, introduce decimal numbers as late as possible. For example, work with cents instead of dollars.