A rational number is a number that can be written in the form p/q (p and q are integers, q is not equal to 0.)
So, an irrational number is a number that cannot be written as the same form.
Rewrite 0.4 as 8/20, 0.5 = 10/20
Therefore, a rational number between the 2 is 9/20, or 0.45
To find an irrational number :
Its decimal places have to be endless (otherwise if it has an end we can multiply with 10^n until the number turns into an integer, making it able to be expressed as p/q)
Its decimal places cannot also be recurring (for example 0.3333.... is recurring), as for example :
0.33333... can be expressed as 1/3
0.16666... can be expressed as 1/6
0.602360236023... can be expressed as 6023/9999 (im not going in details about why it's such but if you want me to then leave a comment.)
So, an irrational number has infinite decimal places and do not have repeating sequences.
-> 0.414114111411111... would be an example.