Real Numbers Book Back Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
5 x 1 = 5
1. If n is a natural number then $\sqrt { n }$ is

(a)

always a natural number

(b)

always an irrational number

(c)

always a rational number

(d)

may be rational or irrational

2. An irrational number between 2 and 2.5 is

(a)

$\sqrt { 11 }$

(b)

$\sqrt { 5 }$

(c)

$\sqrt { 2.5 }$

(d)

$\sqrt { 8 }$

3. The number $0.\bar { 3 }$ in the form $\frac { p }{ q }$ where p and q are integers and $q\neq 0$

(a)

$\frac { 33 }{ 100 }$

(b)

$\frac { 3 }{ 10 }$

(c)

$\frac { 1 }{ 3 }$

(d)

$\frac { 3 }{ 100 }$

4. The value of  $0.\bar { 23 } +0.\bar { 22 }$ is

(a)

$0.\bar { 43 }$

(b)

0.45

(c)

$0.4\bar { 5 }$

(d)

$0.\bar { 45 }$

5. Find the odd one out of the following

(a)

$\sqrt { 32 } \times \sqrt { 2 }$

(b)

$\frac { \sqrt { 27 } }{ \sqrt { 3 } }$

(c)

$\sqrt { 72 } \times \sqrt { 8 }$

(d)

$\frac { \sqrt { 54 } }{ \sqrt { 18 } }$

6. 3 x 2 = 6
7. Represent the following as decimal form
(i) $\frac { -4 }{ 11 }$
(ii) $\frac { 11 }{ 75 }$

8. Convert the following decimal numbers in the form of $\frac { p }{ q } (p,q\in Z\quad and\quad q\neq 0)$
(i) $0.\overline { 3 }$
(ii) $2.12\overline { 4 }$
(iii) $0.4\overline { 5 }$
(iv) $0.\overline { 568 }$

9. Can we write 0.25 as 0.250000 ...? Can a terminating decimal be written as a recurring decimal?

10. 3 x 3 = 9
11. Express the following decimal expression into rational numbers. 0.86

12. Express the following decimal expression into rational numbers $17.2\overline { 15 }$

13. Find the decimal expansion of $\sqrt { 3 }$

14. 2 x 5 = 10
15. Find any two irrational numbers between $\sqrt { 2 }$ and $\sqrt { 3 }$

16. Express $\frac { 1 }{ 33 }$the rational number in recurring decimal form by using the recurring decimal expansion of $\frac { 1 }{ 11 }$. Hence write in recurring decimal form