**Question:**

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 $6.375738$

**Solution:**

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………