Question

find two rational no between 0.12 and 0.13

Answer 1

Let a = 0.12 and b = 0.13.

Clearly, a and b are rational numbers.
We observe the numbers a and b: a and b have 1 in the first place of decimal, but in the second place of decimal a has 2 and b has 3. So, we consider the numbers:

c = 1.201001000100001... 

and, d = 1.2101001000100001... 

Clearly, c and d are irrational numbers such that a < c < d < b.

Answer 2

We can also say that,
0.12 = $\frac{12}{100}$

0.13 = $\frac{13}{100}$

There fore we will multiply the numerator and denominator of both the numbers by 100.

Hence we get, 
$\frac{1200}{10000} and \frac{1300}{10000}$

Now you can easily pic out any two rational numbers between them like: 
$\frac{1201}{10000} and \frac{1202}{10000}$

Now convert them into decimal form:
i.e.  0.1201 and 0.1202