Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution:

Let us find the decimal expansion of 5/7 and 9/11 using long division method.

5/7 = 0.714285

9/11 = 0.81

We can write 3 irrational numbers between 5/11 and 9/11 or 0.714285 and 0.81 are as follows:

(i) 0.721722172221 . . . 

(ii) 0.750975009750009 . . . 

(iii) 0.808008000 . . . 

☛ Check: NCERT Solutions Class 9 Maths Chapter 1

Video Solution:

Find three irrational numbers between the rational numbers 5/7 and 9/11

NCERT Solutions Class 9 Maths Chapter 1 Exercise 1.3 Question 8:

Summary:

The three irrational numbers between the rational numbers 5/7 and 9/11 are 0.721722172221...,0.750975009750009..., and 0.808008000...

☛ Related Questions:

• Express 0.99999 .... in the form of p/q. Are you surprised with your answer? With your teacher and classmates discuss why the answer makes sense?
• What can be the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17? Perform the division to check your answer.
• Look at the several examples of rational numbers in the form p/q (q ≠ 0) where p and q are integers with no common factors other than 1 and having terminating decimal representation (expansions). Can you guess what property q must satisfy?
• Write three numbers whose decimal expansions are non terminating and non-recurring.