#### Real Numbers Two Marks Questions

9th Standard

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Maths

Time : 00:45:00 Hrs
Total Marks : 30
15 x 2 = 30
1. Express the following in the form  ${p\over q},$  where p and q are integers and q $\ne$ 0.
$0.2\overline{45}$

2. Without actual division classify the decimal expansion of the following numbers as terminating or non-terminating and ·recurring.
${17\over 200}$

3. Express the following in the form 3n: 243

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

5. Express the surds in the simple form $\sqrt { 27 }$

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

7. Find any five rational numbers between
(i) $\frac { 1 }{ 4 }$ and $1\over 5$
(ii) 0.1 and 0.11
(iii) -1 and -2

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. Find whether x and y are rational or irrational in the following
(i) a = 2 + $\sqrt { 3 }$ , B = 2 - $\sqrt { 3 }$ ; x = a + b,Y = a+ b
(ii) a = $\sqrt { 2 }$  + 7, B = $\sqrt { 2 }$ - 7 ; x = a + b, Y = a - b
(iii) a = $\sqrt { 75 }$, b = $\sqrt { 3 }$, x = ab, y = $\frac { a }{ b }$
(iv) a = $\sqrt { 18 }$, b = $\sqrt { 3 }$, x = ab, y = $\frac { a }{ b }$

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

11. Convert the following rational numbers into decimal
(i) $3\over 4$
(ii) $5\over 8$
(iii) $9\over 25$

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

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

14. Create a word problem whose solution is an irrational number.

15. Find any 3 irrational numbers between 0.12 and 0.13.