#### Real Numbers Model Question Paper

9th Standard

Reg.No. :
•
•
•
•
•
•

Maths

Time : 01:30:00 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. 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. $0.\overline { 34 } +0.3\bar { 4 }$ =

(a)

$0.6\overline { 87 }$

(b)

$0.\overline { 68 }$

(c)

$0.6\bar { 8 }$

(d)

$0.68\bar { 7 }$

5. Which one of the following has terminating decimal expansion?

(a)

$\frac { 7 }{ 9 }$

(b)

$\frac { 8 }{ 15 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 5 }{ 32 }$

6. The value of $\bar { 0.03 }$ +$\bar { 0.03 }$  is ___________.

(a)

$\bar { 0.09 }$

(b)

$\bar { 0.09 }$

(c)

$\bar { 0.09 }$

(d)

0

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. 7 x 2 = 14
14. Find any three rational numbers between $\frac { -7 }{ 11 }$and $\frac { 2 }{ 11 }$

15. Express the rational number $\frac { 1 }{ 27 }$  in recurring decimal form by using the recurring decimal expansion of $1\over3$ . Hence write$\frac { 59 }{ 27 }$ in recurring decimal form.

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

17. Verify that 1 = $0.\overline { 9 }$

18. We used to write $\sqrt{2}=1.414=\frac{1414}{1000}.$ Can we say  $\sqrt{2}$  is a rational number?

19. Give any two rational numbers lying between 0.5151151115…. and 0.5353353335…

20. Find any 4 irrational numbers between $\frac { 1 }{ 2 }$ and $\frac { 2 }{ 3 }$

21. 5 x 3 = 15
22. Express the following decimal expression into rational numbers. $0.\overline { 24 }$

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

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

25. Simplify;$\sqrt { 44 } +\sqrt { 99 } -\sqrt { 275 }$

26. Write in scientific notation ;(60000000)3

27. 2 x 5 = 10
28. Find any two irrational numbers between$\frac { 6 }{ 7 }$ and $\frac { 12 }{ 13 }$

29. Represent the following numbers on the number line.
(i) 5.348
(ii) $6.\bar { 4 }$ up to 3 decimal places
(iii) $4.\bar { 73 }$  upto 4 decimal places