Verified answer

Answer:

5/7 can be written as 0.̅7̅1̅̅4̅̅2̅8̅̅5̅

9/11 can be written as 0.̅8̅̅1̅

Hence the three different irrational numbers that lies between the rational numbers 5/7 and 9/11 are:

0.727227222…, 0.757557555…… and 0.808008000…..

Answer:

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 . . .