How to transform a Infinite decimal of $\frac{23}{6}$ into binary?
Here is a hint by example. 

$\frac{23}6 &gt; 2$
$\frac{23}6-2 = \frac {11}6 &gt; 1$
$\frac{11}6-1 = \frac {5}6 &gt; \frac 12$
$\frac{5}6-\frac12 = \frac {1}3 &gt; \frac 14$
$\frac{1}3-\frac14 = \frac {1}{12} &gt; \frac 1{16}$
$\vdots$

So $\frac{23}6=2+1 +\frac12+\frac14+\frac1{16}+\cdots=(11.1101\cdots)_2$





Exercise. How to determine the period of the fraction part of the binary expansion of $\frac {23}6$?