Insert a rational number and an irrational number between the following
(i) 2 and 3
(ii) 0 and $0.1$
(iii) $1 / 3$ and $1 / 2$
(iv) $-2 / 5$ and $-1 / 2$
(v) $0.15$ and $0.16$
(vi) $\sqrt{2}$ and $\sqrt{3}$
(vii) $2.357$ and $3.121$
(viii) 0001 and 001
(ix) $3.623623$ and $0.484848$
(x) $3.375289$ and $6.375738$
We know that, there are infinitely many rational and irrational values between any two numbers.
(i) A rational number between 2 and 3 is 2.1.
To find an irrational number between 2 and 3. Find a number which is non-terminating non-recurring lying between them.
Such number will be 2.040040004…………..
(ii) A rational number between 0 and 0.1 is 0.03.
An irrational number between 0 and 0.1 is 0.007000700007……….
(iii) A rational number between 1/3 and 1/2 is 5/12. An irrational number between 1/3 and 1/2 i.e., between 0-3 and 0.5 is 0.4141141114………….
(iv) A rational number between -2/5 and 1/2 is 0. An irrational number between -2/5 and 1/2 i.e., between – 0.4 and 0.5 is 0.151151115………..
(v) A rational number between 0.15 and 0.16 is 0.151. An irrational number between 0.15 and 0.16 is 0.1515515551…….
(vi) A rational number between √2 and √3 i.e.,, between 1.4142…… and 1.7320…… is 1.5.
An irrational number between √2 and √3 is 1.585585558……….
(vii) A rational number between 2.357 and 3.121 is 3. An irrational number between 2.357 and 3.121 is 3.101101110……..
(viii) A rational number between 0.0001 and 0.001 is 0.00011. An irrational number between 0.0001 and 0.001 is 0.0001131331333………..
(ix) A rational number between 3.623623 and 0.484848 is 1. An irrational number between 3.623623 and 0.484848 is 1.909009000……….
(x) A rational number between 6.375289 and 6.375738 is 6.3753. An irrational number between 6.375289 and 6.375738 is 6.375414114111………
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.