#### Real Numbers Model Question Paper

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
5 x 1 = 5
1. Which one of the following has terminating decimal expansion?

(a)

$\frac { 7 }{ 9 }$

(b)

$\frac { 8 }{ 15 }$

(c)

$\frac { 1 }{ 2 }$

(d)

$\frac { 5 }{ 32 }$

2. Irrational number has a________________ .

(a)

terminating decimal

(b)

no decimal part

(c)

non-terminating and recurring decimal

(d)

non-terminating and non-recurring decimal

3. $\sqrt [ 3 ]{ 192 } +\sqrt [ 3 ]{ 24 }$

(a)

$3\sqrt [ 3 ]{ 6 }$

(b)

$6\sqrt [ 3 ]{ 3 }$

(c)

$\sqrt [ 3 ]{ 216 }$

(d)

$\sqrt [ 6 ]{ 216 }$

4. When $\left( 2\sqrt { 3 } -\sqrt { 5 } \right) ^{ 2 }$ is simplified, we get

(a)

17

(b)

$\sqrt { 15 }$

(c)

$17-4\sqrt { 15 }$

(d)

$4\sqrt { 15 }$

5. The length of a square is 1.2X103 m. Its area is_______

(a)

14.4 X 106

(b)

1.44 X 106

(c)

0.144 X 10

(d)

1440

6. 5 x 2 = 10
7. Find three different irrational numbers between the rational numbers  $\frac { 5 }{ 7 }$ and $\frac { 9 }{ 11 }$

8. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
$7\over 16$

9. Use a fractional index to write $\left( 5\sqrt { 125 } \right) ^{ 7 }$

10. Can you reduce the following numbers to surds of same of same order $\sqrt { 5 }$

11. Express the surds in the simple form $\sqrt [ 3 ]{ 128 }$

12. 5 x 3 = 15
13. Arrange in ascending order:$\sqrt [ 3 ]{ 5 } ,\sqrt [ 4 ]{ 7 } ,\sqrt [ 2 ]{ 6 }$

14. Express the following surds in its simple form $\sqrt [ 4 ]{ 324 }$

15. Substract $6\sqrt { 7 }$ from $9\sqrt { 7 }$ . Is the answer rational or irrational?

16. Compute and give the answer in the simplest form;$3\sqrt { 162 } \times 7\sqrt { 50 } \times 6\sqrt { 98 }$

17. Write in scientific notation:(500000)5X(3000)3

18. 4 x 5 = 20
19. Find any  seven rational numbers between $\frac { 5 }{ 8 }$ and $\frac { 5 }{ 6 }$

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

21. Represent $-\frac { 2 }{ 11 } ,-\frac { 5 }{ 11 } and-\frac { 9 }{ 11 }$on the number line.

22. Classify the numbers as rational or irrational
(i) $\sqrt { 10 }$
(ii) $\sqrt { 49 }$
(iii) 0.025
(iv) $0.7\overline { 6 }$
(v) 2.505500555...
(vi) $\frac { \sqrt { 2 } }{ 2 }$