Question

Irrational number between 0.12 and 0.13

Answer 1

Irrational numbers are the numbers which cannot be expressed in the p/q form
Irrational numbers between them are:
0.121212121212121.....
0.12512612712812912012151216.......
0.122122312234122345....

Answer 2

Irrational numbers cannot be expressed in the form of $\bold{\frac{p}{q}}$.

Given:

0.12 and 0.13

To find:  

Irrational numbers between 0.12 and 0.13 = ?

Solution:  

Firstly change the decimal numbers into p/q form we get 12/100 and 13/100

Now to find the irrational numbers, irrational numbers are those numbers which after decimal do not have any pattern repetition among them and can’t form p/q form as formed above with 0.12 and 0.13, therefore, irrational number between 0.12 and 0.13 can be

0.121001000100001000000100000100000100011100010………………………….

0.12000010000101010010001110000101100100000100000111111000000……….

Numbers like these which are random and have no repetition pattern after the decimal. Cannot be expressed in the form of $\bold{\frac{p}{q}}$