$1.1101101*2^{^{-3}}$ we convert it to 0.0011101101 (How?)
Remember that for Binary multiplication we increase number of bit by shifting decimal point to right and for Binary division we decrease number of bits by shifting decimal point to left.
To get the fractional value assume we are given number as 11101101 ignoring 0's coming before first 1 but after decimal point.
now calculate decimal value of 11101101 which is 237. now divide it by $2^{^{N}}$ where N is number of bit after decimal point
(of course we will count number of bits till only right most 1). Here N is 10. so $\frac{237}{2^{^{10}}}= 0.231445$ or 2.31*$10^{^{-1}}$. but since it is not given and also we are asked to give closest value which is 2.27*$10^{^{-1}}$.
you might have wondering how this is producing same result. well there is no some trick. In fact you will get same $\frac{237}{1024}$ if you just add the p/q forms.
$\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{128}+\frac{1}{256}+\frac{1}{1024}=\frac{237}{1024}$
i just found first method much easier rather than calculating fractional value separately of each term and then adding them all. Let me know if it helps.