Question

Find 2 rational and an irrational number in between 0.232332333233332... and

0.252552555255552...

Answer 1

Let a = 0.232332333233332

b = 0.252552555255552

Since the decimal representations of a and b are non-terminating and non-repeating, it follows that a and b are irrational numbers. Again the first place of decimal of a and b are equal, and second place of b is greater than a.

a < b

We have to find number between a and b such that it is greater than a and less

than b, and irrational. Now considering the following numbers

0.232442333233332......
0.232442333233332.....

​​We can find many numbers like this.

Rational Numbers.

Rational numbers can be expressed of form p/q . So we can find numbers between a and b like 0.24 (24/100) and 0.242 (242/1000)

These numbers lie between a and b and can be represented by the form p/q hence are rational.