# Question Bank For Rational Numbers

Q1. Identify the following into rational or irrational :

(i) \sqrt { 18 } (ii) 2+\sqrt { 3 } (iii) { \left( 2+\sqrt { 2 }  \right)  }^{ 2 } (iv) \frac { 1 }{ 2 } \sqrt { 7 }  (v) 1.125

(vi) \frac { \pi  }{ 2 } (vii) 1.\bar { 2 } (viii) \sqrt { 9 } +\sqrt { 4 } (ix) 1.1211211121111 …

Ans- (i) Irrational number (ii) Irrational number (iii) Irrational number

(iv) Irrational number (v) Irrational number (vi) Irrational number

(vii) Irrational number (viii) Irrational number (ix) Irrational number

Q2. Is { \left( 5+\sqrt { 3 }  \right)  }^{ 2 }+{ \left( 5-\sqrt { 3 }  \right)  }^{ 2 } is rational number? Justify.

Ans- Yes, rational(56)

Q3. Give an example to show that product of a rational number and an irrational number many be a rational number.

Ans- Example: 0\times \left( \sqrt { 7 } +2 \right) =0

Q4. Give an example to show that product of two irrational numbers and to be an irrational number.

Ans- (i) Product of \left( 2+\sqrt { 3 }  \right) \quad and\quad \left( 2-\sqrt { 5 }  \right) which is irrational

(ii) Product of \left( 3+\sqrt { 3 }  \right) \quad and\quad \left( 3-\sqrt { 5 }  \right) which is rational.

Q5. Find the product of \left( 1+3\sqrt { 2 }  \right) and\left( 1-3\sqrt { 2 }  \right) . Is the product rational or irrational?

Ans- Product= -17(rational).

Q6. Find a rational number lying between

(i) \frac { 1 }{ 4 } and\frac { 1 }{ 3 } (ii) \frac { 3 }{ 8 } and\frac { 2 }{ 5 } (iii) 1.3 and 1.4

(iv) 0.75 and 1.2 (v) -1 and \frac { 1 }{ 2 }  (vi) -\frac { 3 }{ 4 } and -\frac { 2 }{ 5 }

Ans- (i) \frac { 7 }{ 24 } (ii) \frac { 31 }{ 80 } (iii) 1.35

(iv) 0.975 (v) –\frac { 1 }{ 4 } (vi) –\frac { 23 }{ 40 }

Q7. Find three rational numbers lying between \frac { 1 }{ 5 } and \frac { 1 }{ 4 }.

Ans- \frac { 17 }{ 80 } ,\frac { 18 }{ 80 } ,\frac { 19 }{ 80 }

Q8. Find five rational numbers lying between \frac { 2 }{ 5 } and \frac { 3 }{ 4 }

Ans- \frac { 55 }{ 120 } ,\frac { 62 }{ 120 } ,\frac { 69 }{ 120 } ,\frac { 76 }{ 120 } ,\frac { 83 }{ 120 }

Q9. Insert six rational numbers between 3 and 4.

Ans- \frac { 22 }{ 7 } ,\frac { 23 }{ 7 } ,\frac { 24 }{ 7 } ,\frac { 25 }{ 7 } ,\frac { 26 }{ 7 } ,\frac { 27 }{ 7 } .

Q10. Insert 16 rational numbers between 2.1 and 2.1.

Ans- 2.105, 2.11, 2.115, 2.12,  2.125, 2.13, 2.135, 2.14, 2.145, 2.15, 2.155,2.16,2.165,2.17,2.175,2.18.

Q11. Without actual division, find which of the following rationals are terminating decimals.

(i) \frac { 13 }{ 80 } (ii) \frac { 7 }{ 24 } (iii) \frac { 5 }{ 12 } (iv) \frac { 8 }{ 35 } (v) \frac { 16 }{ 125 }.

Ans- \frac { 13 }{ 80 } , \frac { 16 }{ 125 }

Q12. Convert each of the following into a decimal.

(i) \frac { 5 }{ 8 } (ii) \frac { 9 }{ 16 } (iii) \frac { 7 }{ 25 } (iv) \frac { 11 }{ 24 } (v) 2\frac { 5 }{ 12 }

Ans-  (i)0.625 (ii) 0.5625 (iii) 0.28 (iv) 0.458\bar { 3 } (v) 2.141\bar { 6 }

Q13. Express each of the following as a fraction in simplest form.

(i) 0.\bar { 3 } (ii) 1.\bar { 3 } (iii) 0.\bar { 34 } (iv) 3.\bar { 14 }.

(v) 0.\bar { 324 } (vi) 0.\bar { 17 } (vii) 0.\bar { 54 } (viii) 0.1\bar { 63 }.

Ans- (i) \frac { 1 }{ 3 }  (ii) \frac { 4 }{ 3 } (iii) \frac { 34 }{ 99 } (iv) \frac { 311 }{ 99 } (v) \frac { 12 }{ 37 } (vi) \frac { 8 }{ 45 } (vii) \frac { 49 }{ 90 } \frac { 9 }{ 55 }.

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