why can't 0.2 (base 10 )be represented in binary as 0.10 (base 2)
<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>