number systems for class 9

MATHEMATICS ASSIGNMENT – IX STEPS … A TCY Program

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STEPS____________________________________________________________ G e t f r e e n o t e s f o r C l a s s X a n d I X o n

w w w . t c yo n l i n e . c o m

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Directions for questions 1 – 15: State true or false.

1. There are infinitely many natural numbers between 1 and 2.

2. The difference between any two consecutive natural numbers is one.

3. There are infinitely many rational numbers.

4. All real numbers are rational numbers.

5. Every point on the real number line can be written in the from n , where ‘n’ is a natural number.

6. Every real number is either rational or irrational.

7. The sum of two irrational numbers is always irrational.

8. Every irrational number can be converted into a rational number.

9. 5 3 and 10 3 are rationalizing factors of each other.

10. Every irrational number has a unique rationalizing factor.

11. The product of am and an is amn.

12. If (–a)n = an, then ‘n’ is an even number.

13. All prime numbers are odd numbers.

14. All decimal numbers with non–terminating decimal parts are irrational numbers.

15. If ‘a’ and ‘b’ are two consecutive integers and ‘a’ lies to the right of ‘b’, then a – b > 0.

16. Write two integers which are not whole numbers.

17. Insert one rational number between 3 and 4.

18. Insert 3 rational numbers between 4 and 5.

19. Insert 4 rational numbers between 52

and 53

.

20. Express 3 and –2 in the form of qp

, where p and q are integers and q ≠ 0.

21. Give two irrational numbers whose sum is rational.

22. Give two irrational numbers whose sum is irrational.

23. Give two irrational numbers whose difference is (i) rational (ii) irrational.

24. Give two irrational numbers whose product is (i) rational (ii) irrational.

25. Give two irrational numbers whose quotient is (i) rational (ii) irrational.

26. Locate 2 and 3 on the number line.

27. Locate the points representing 2 + 1 and 2 –1 on the number line.

ASSIGNMENT ON NUMBER SYSTEMS


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28. Construct a square root spiral starting from 2 upto 5 .

29. Classify the following rational number into numbers with

(i) terminating decimal expansion

(ii) non–terminating decimal expansion.

(a) 41

(b) 31

(c) 53

(d) 73

30. Find the decimal representation of 243

and 353

31. State which of the following fractions are convertible into terminating decimals, doing actual division.

(a) 1833

(b) 254

(c) 155

(d) 135

32. Write two numbers whose decimal expansion are non–terminating and non repeating.

33. Convert the following decimal numbers into rational number in the form qp

.

(i) 0.08 (ii) 1.205 (iii) 0.001 (iv) 3.2125

34. Convert the following decimal numbers into rational numbers in the form p/q.

(i) 0. 312 (ii) 0. 092 (iii) 0.12345 (iv) 0.4 (v) 2.21 347

35. Find four irrational number between 31

and 32

.

36. Find four irrational numbers between 4 and 5.

37. Classify the following numbers as rational or irrational

(i) 26 (ii) 324 (iii) 0.125 (iv) 0.934984….. (v) 4.02121121112………..

38. Visualize 2.34 on the number line using successive magnification.

39. Visualize 4. 3 on the number line upto three decimal places using successive magnification.

40. Find the sum of (3 + 4 3 + 5 2 )

41. Simplify:

(i) (5 2 + 7 3 ) – (3 2 + 2 3 ) (ii) 5 2 × 2 10 × 5 15

(iii) 5 3 × 7 3 × 2 2 × 3 2 (iv) 32

36

42. Find the simplest rationalizing factors of the following irrationals.

(i) 8 (ii) 183 (iii) 5 12 (iv) 7 7

43. Rationalize the denominators of the following.

(i) 3

1 (ii)

23

2

− (iii)

13

1

−


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44. If a = 3 12 + 2 18 and b = 2 + 3 , find the value of

(i) a + b (ii) a – b (iii) 2a + 3b (iv) 5a – 4b

45. Rationalize the denominators

(i) 310

35

− (ii)

26

23

−

46. Evaluate

(i) 4–5 × 48 ÷ 47 (ii) 57 × 53 ÷ 5–2

(iii) (32)3 × (3–2)2 (iv) 0

2856

⎟⎠⎞

⎜⎝⎛ ×

11×

169

52 2

×⎟⎠⎞

⎜⎝⎛

(v) 4/3)625( − (vi) 5/3

321 −

⎟⎠⎞

⎜⎝⎛

47. Evaluate

(i) (243)3/5 ÷ (64)–1/4 (iii) 181/2 × 81/2 (iv) 3/1

2/1

88

48. Find the point representing 5.3 on the number line geometrically.

49. Find the point representing 42 on the number line geometrically.

50. Find the point representing 35 on the number line geometrically.

51. In the following figure, AB = 7 units, BC = 5 units and AC is the diameter of the semicircle. What is the

value of ‘x’?

52. In the figure, PQ = 12, QS = 6 and PR is the diameter of the semicircle. Find PR.

a

D

A B 7 C 5

x b

x

S

P Q 12 R

6 y


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4

53. In the figure, ‘O’ is the origin of the number line ‘ l ’. AB = 1 unit and AB ⊥ l . The semi circle with

centre origin and radius OB intersects the line at ‘C’ and ‘D’. Find the numbers represented by ‘C’ and

‘D’.

54. Look at the square root spiral shown below. Given that P1P2 = P2P3 = P3P4 = P4P5 = 1 unit. Find the

length of the segment OP5.

55. In the figure, ‘O’ is the centre of the number line ‘ l ’. AB ⊥ l and CD ⊥ l . AB = 1 unit, the arc with

centre ‘O’ and radius OB intersects the line at ‘C’. CD = 2 units, the arc with centre ‘O’ and radius OD

intersects the line at ‘E’. Find the number that represents the point E. Check whether E represents a

natural number.

56. In the figure, ‘O’ is the centre of the number line ‘ l ’, OA = 6 and OC = 7. An arc with centre ‘O’ and

radius OC intersects the perpendicular on A and ‘B’. Find AB.

P2

2 O P1 3 4 5

P3

P4 P5

1 O C

2 A

B

3 4 5 6 7 l 3

x

B

D 1 O C

1

2 3

A

B

1 O E 2 C

D

A


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5

57. In the figure, ‘O’ is the centre of the number line ‘ l ’. A semi circle is drawn with centre ‘O’ and radius

10 units. The semi circle intersects the perpendiculars at the points A and B, respectively represent –6

and 5, at D and C. Calculate the area of the quadrilateral ABCD.

(Take 3 =1.732)

D C

A B –12 –10 –8 –6 –4 –2 O 2 4 6 8 10 12 5

l


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6

NUMBER SYSTEMS

ANSWER KEY

1. False 2. True 3. True

4. False 5. False 6. True

7. False 8. True 9. True

10. True 11. True 12. True

13. False 14. False 15. True

16. (–2, –3) 20. ⎟⎠⎞

⎜⎝⎛ −

2

4,

2

6

21. (3– 5 , 4 + 5 )

22. ( 2 , 3 )

23. (i) 3 + 5 , 2 + 5

(ii) 3 + 5 , 2 + 2 5

24. (i) 2 5 , 5 (ii) 2 3 , 2

25. (i) 2 , – 2 , 2 , 3

29. (i) (a), (c) (ii) (b), (d)

30. [0.125, 0. 0857143]

31. (b)

33. (i) 25

2 (ii)

200

241

(iii) 1000

1 (iv)

80

257

34. (i) 333104

(ii) 99992

(iii) 33334115

(iv) 52

(v) 49950

110563

37. (i) Irrational (ii) Rational

(iii) Rational (iv) Irrational

(v) Irrational

40. 5

41. (i) 2 2 + 5 3 (ii) 500 3

(iv) 1260 (iv) 3

42. (i) 2 (ii) 2

(iii) 3 (iv) 7

43. (i) 3

3 (ii) 2( 3 + 2 )

(iii) 2

13 +

44. (i) 7 3 + 7 2

(ii) 5 3 + 5 2

(iii) 15 3 + 15 2

(iv) 26 3 + 26 2

45. (i) 7

)330(5 + (ii)

2

)13(3 +

46. (i) 4–4 (ii) 512

(iii) 32 (iv) 100

9

(v) 125

1 (vi) 8

47. (i) 216 (ii) 12 (iii) 2

51. 35 52. 15

53. 10 , – 10 54. 2 5

55. 7 , No 56. 13

number systems for class 9

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