Representation of real numbers in Genetic Algorithm Take a look at section 2.2.2 of this book (from Page-15 to 16).


  2.2.2 Representation and Evaluation  
  
  $$max f (x)= x sin(10πx)+2.0 ... ... ... (2.8)$$
  $$s.t. −1 ≤ x ≤ 2$$
  
  We can use a real number, in the range $[−1,2]$, to represent a solution in Eq. $2.8$ directly. Many operators can handle real number representation. But we use the binary code or binary representation here for two reasons. GAs were originally proposed to be binary code to imitate the genetic encoding of natural organisms. On the other hand, binary code is good for pedagogy. A binary chromosome is necessary to represent a solution x in the scale $[−1,2]$. The same holds for the binary representation of real numbers in a computer.  
  
  In binary code, we cannot represent a real number completely correctly, so a
  trade-off is necessary. A tolerance needs to be deﬁned by the user, which means the errors below the tolerance are extraneous. If we divide the deﬁnition domain into $2^1 = 2$ parts evenly and select the smallest number in the parts to represent any number in the division, we can only represent $−1$ and $0.5$ by $0$ and $1$ respectively. $2^2 = 4$ divisions make the $00$, $01$, $10$, and $11$ represent $−1$, $−0.25$, $0.5$, and $1.25$, respectively. The larger division number we select, the less error there is in representing a real number on binary code. Suppose we use $100$ binary codes to represent a real number in the range $[−1,2]$; the maximum error is $\frac{3}{2100} ≈ {2.37}^{−30}$, which would be satisfactory for most users. In this way, we can represent a real number with any accuracy requirements. 
  
  In this problem, we use $l = 12$ binary codes to represent one real number as follows, which constitutes a chromosome to be evolved.


Actually, I haven't understood this text. I know that binary numbers are already able to represent fractions.

So, what are they talking about?
The authors want to use a binary genome which contains specific interpretation/mapping to a fixed precision real number. They could use one or more existing schemes, but these typically won't represent the exact precision and range of real numbers they want to use in the example problem. 

They use their own encoding scheme and explain it in the text for completeness. Any similarities between their scheme and other binary representations of real numbers are to be expected, and if you understand them, it will help understand what they are doing here too.

GAs don't have to use this sort of scheme for real numbers. Often they use standard floating-point representation as separate elements. But the authors want a binary code here to help teach some basic concepts, which is what they mean by "on the other hand, binary code is good for pedagogy"