1.

Inset 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 , (iv) `sqrt6 and sqrt3` (vii) 2.357 and 3.121 , (vii) .0001 and .001 (ix) 3.623623 and 0.484848 , (x) 3.375289 and 6.375738

Answer» 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-terminatiing non-recuring 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.bar3and 0.5 is 0.141141114......`
(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 a nd 0.16 is 0.151. An irrational number between 0.15 and 0.16 is 0.1515515551.....
(vi ) A rational number between `sqrt2 and sqrt3` i.e between 1.4142 ....... and 1.7320....... is 1.5.
An irrational number between `sqrt2 and sqrt3` 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 6.3754141141111........


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