title: why can't 0.2 (base 10 )be represented in binary as 0.10 (base 2)
body: <p>I've been reading about floating point types in java such as double.
  I've also been reading about converting fractions to binary and how to do it.
  I can do the math and find that representing 0.2 in binary is the following approximation: </p>
  
  <pre><code>0.00110011001100...
  </code></pre>
  
  <p>However 2 in binary is 10.
  So why can't I just say that 0.2 (base 10 ) is equivalent to 0.10 (base 2)?</p>
  
  <p>I've read a similar <a href="https://stackoverflow.com/questions/1089018/why-cant-decimal-numbers-be-represented-exactly-in-binary">question</a>, but I'm still confused by this</p>
  
  <p>Another example would be something like 5.8</p>
  
  <pre><code>101.110011001100...
  </code></pre>
  
  <p>Why couldn't we do: 101.1000 since 8 in binary is 1000</p>
  
  <p>I understand that 0.10 and 0.1000 are the same, but in this context they would be separate.</p>