#### Real Numbers Important Questions

9th Standard

Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 50
6 x 1 = 6
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. Which one of the following, regarding sum of two irrational numbers, is true?

(a)

always an irrational number

(b)

may be a rational or irrational number

(c)

always a rational number

(d)

always an integer.

3. An irrational number between 2 and 2.5 is

(a)

$\sqrt { 11 }$

(b)

$\sqrt { 5 }$

(c)

$\sqrt { 2.5 }$

(d)

$\sqrt { 8 }$

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. $0.\overline { 34 } +0.3\bar { 4 }$ =

(a)

$0.6\overline { 87 }$

(b)

$0.\overline { 68 }$

(c)

$0.6\bar { 8 }$

(d)

$0.68\bar { 7 }$

6. The decimal form of -$\frac { 3 }{ 4 }$ is_______________

(a)

- 0.75

(b)

- 0.50

(c)

-0.25

(d)

- 0.125

7. 5 x 1 = 5
8. The value of $3\sqrt { 3 } +\sqrt { 3 }$ is ______________.

()

$4\sqrt { 3 }$

9. The value of $\left[ \sqrt { { x }^{ 3 } } \right] ^{2/3}$ is

()

x

10. If $\sqrt { 10 }$= 3.1622, then the value of is $\frac { 1 }{ \sqrt { 10 } }$ is_________.

()

0.31623

11. The rational number equivalent to $\frac { 5 }{ 9 }$ such that its numerator is 25 is____________ .

()

$\frac { 25 }{ 45 }$

12. Divide $15\sqrt { 12 }$ by $3\sqrt { 3 }$the result is ___________.

()

10

13. 10 x 2 = 20
14. Express the following in the form ${p\over q},$ where p and q are integers and q $\ne$ 0.
$0.\overline {47}$

15. Find three different irrational numbers between the rational numbers  $\frac { 5 }{ 7 }$ and $\frac { 9 }{ 11 }$

16. Evaluate : 10 -4

17. Find the value of  ${ 625 }^{ \frac { 3 }{ 4 } }$

18. Find any three rational numbers between $\frac { -7 }{ 11 }$and $\frac { 2 }{ 11 }$

19. Represent the following as decimal form
(i) $\frac { -4 }{ 11 }$
(ii) $\frac { 11 }{ 75 }$

20. 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) $0.\overline { 568 }$

21. Convert the following rational numbers into decimal
(i) $2\over 3$
(ii) $47\over 99$
(iii) $-{16\over 45}$

22. We used to write $\pi$ as $\frac{22}{7}.$ Can we say $\pi$ is a rational number?

23. Find any 4 irrational numbers between $\frac { 1 }{ 4 }$ and $\frac { 1 }{ 3 }$

24. 3 x 3 = 9
25. Represent $\sqrt { 9.3 }$ on a number line

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

27. Sho that $\sqrt [ 3 ]{ 2 } >\sqrt [ 5 ]{ 3 }$

28. 2 x 5 = 10
29. Find any two irrational numbers between$\frac { 6 }{ 7 }$ and $\frac { 12 }{ 13 }$

30. Find any three rational numbers between $\frac { 1 }{ 2 }$ and $\frac { 1 }{ 5 }$