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) √2 and √3 (vii) 2.357 and 3.121 (viii) 0.0001 and 0.001 (ix) 3.623623 and 0.484848 (x) 6.375289 and 6.375738

Answer 1

A rational number between.

1) 2.5

2) 0.01

3) 0.4

4) 0

5) 0.151

6) 1.15

7) 2.358

8)0.00011

9) 1

10) 6.3753

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Answer 2

Answer:

(i) 2 and 3 So, rational number between 2 and 3 = 2.5 And, irrational number between 2 and 3 = 2.040040004…

(ii) 0 and 0.1 So, rational number between 0 and 0.1 = 0.05 And, irrational number between 0 and 0.1 = 0.007000700007…

(iii) 1/3 and 1/2 LCM of 3 and 2 is 6. 1/3 = 0.33 1/3 can be written as (1 × 20)/(3 × 20) = 20/60 ½ = 0.5 1/2 can be written as (1 × 30)/(2 × 30) = 30/60 So, rational number between 1/3 and 1/2 = 25/60 And, irrational number between 1/3 and 1/2 = irrational number between 0.33 and 0.5 = 0.414114111…

(iv) – 2/5 and 1/2 LCM of 5 and 2 is 10. -2/5 = -0.4 -2/5 can be written as (-2 × 2)/(5 × 2) = -4/10 1/2 = 0.5 1/2 can be written as (1 × 5)/(2 × 5) = 5/10 So, rational number between -2/5 and 1/2 = rational number between -4/10 and 5/10 = 1/10 And, irrational number between -2/5 and 1/2 = irrational number between -0.4 and 0.5 = 0.151151115...

(v) 0.15 and 0.16 Rational number between 0.15 and 0.16 = 0.151 Irrational number between 0.15 and 0.16 = 0.151551555…

(vi) √2 = 1.41 and √3 = 1.732 Rational number between √2 and √3 = rational number between 1.41 and 1.732 = 1.5 Irrational number between √2 and √3 = irrational number between 1.41 and 1.732 = 1.585585558…

(vii) 2.357 and 3.121 Rational number between 2.357 and 3.121 = 3 Irrational number between 2.357 and 3.121 = 3.101101110…

(viii) .0001 and .001 Rational number between .0001 and .001 = 0.00011 Irrational number between .0001 and .001 = 0.0001131331333…

(ix) 3.623623 and 0.484848 Rational number between 3.623623 and 0.484848 = 1 Irrational number between 3.623623 and 0.484848 = 1.909009000…

(x) 6.375289 and 6.375738. Rational number between 6.375289 and 6.375738 = 6.3753 Irrational number between 6.375289 and 6.375738 = 6.375414114111…

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