Question

Find two rational and two irrational numbers between 2 and 5.

Answer 1

Hint: At first, define both types of numbers, then find the numbers according to their respective properties either rational/irrational numbers.

Complete step-by-step answer:
We have been asked to find two rational and irrational numbers between 2 and 5. So at first, we will explain what a rational and irrational number is. In Mathematics, a rational number is a number that can be expressed as the quotient or the fraction \[\dfrac{p}{q}\] of two integers where p is the numerator and q is a non-zero denominator. Since q may be equal to 1, every integer is a rational number. The set of all rational numbers is often referred to as “the rationales”. For example, \[\dfrac{7}{3},2,1,\dfrac{5}{7},\text{ etc}\text{.}\]The decimal expansion of a rational number is always either terminates after a finite number of digits or begins to repeat the same finite sequence of the digits over and over. Moreover, any repeating or terminating decimal represents a rational number. For example: 0.25, 0.5, 0.8333, etc. In Mathematics, the irrational numbers are all the real numbers which are not rational numbers. The decimal expansion of irrational numbers is non-terminating as well as non – repeating. They can also be expressed as non – terminating continued fractions. For example, \[\sqrt{2}\], 2.345678…., 0.3030030003….., etc.
So, now we are asked to find two rational numbers between 2 and 5 which can be written as 3, 4, and two irrational numbers which can be written as 3.141592….. and 4.238727…..

Note: Students while solving questions on rational and irrational numbers from books, they generally confuse as their answers don’t match. This is because between any two integers, there are infinite rational and irrational numbers.