Representing 0.1 (or rather, 1/10) has the same problem in binary that representing 1/3 has in decimal. Your denominator doesn't divide any power of your radix,

Representing 0.1 (or rather, 1/10) has the same problem in binary that representing 1/3 has in decimal. Your denominator doesn't divide any power of your radix, so your representation has to be either infinite, or inaccurate. If you've ever tried to do complex decimal math by copying results like 0.6666667 into and out of a calculator, you've probably run into the same issues.