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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 |
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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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