mathematics - number system

Class 9 - Mathematics

Number System

MCQ
Q&A
Question:
Express each of the following numbers in the form p/q.
(i) 15.75 0 (ii) 8.0025 (iii) -24.6875
Answer:

(i) We have,
15.75 = 1575/100
=> (1575 x 25)/(100 x 25)= 63/4

(ii)We have,
8.0025 = 80025/10000 = (80025 x 25)/(1000 x 25) = 3201/400

(iii) We have,
-25.6875 = -256875/10000 = (-256875 ÷ 625)/(1000 ÷625) = -411/16

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Questions and Answers


Number System - Questions
1. If 9 n 3 2 3 -n/2 -2 27 n 33m 23 = 1 27 , Prove that m - n = 1.
Answer
2. Prove that: a -1 a -1 + b -1 + a -1 a -1 b -1 = 2b 2 b 2 a 2
Answer
3. Find the value of x, if 5 x-3 × 3 2x-8 =8
Answer
4. if x,y,z are positive real numbers show that :

x -1 y . x -1 z . z -1 x
Answer
5. Show that :

x a(b-c) x b(a-c) x b x a c = 1 (ii) x a+b 2 x b+c 2 x c+a 2 (xaxbxc)4 = 1
Answer
6. Simplify : 81 16 -3/4 × 25 9 -3/2 ÷ 5 2 -3
Answer
7. If a = 2 and b= 3, then find the values of each of the following :

(i) aa + bb (ii) ab + ba (iii) ab

(iv) (a/b)a (v) (1/a +1/b)a
Answer
8. Evalute each of the following:

(i) (2/11)4 x (11/3)2 x (3/2)3 (ii) (1/2)5 x (-2/3)4 x (3/5)-1

(iii) 255 x 260 - 297 x 218 (iv) (2/3)2 x (2/5)-3 x (3/5)2
Answer
9. Evalute each of the following:

(i) 52 x 54 (ii) 58 53 (iii) (32)3 (iv) (11/12)3 (v) (3/4)-3
Answer
10. Simplify each of the following :

(i) (625)-1/4 (ii) (256/81)5/4 (iii) (243/32)-4/5 (iv) 5√(32)-3
Answer
11. Simplify :

(i) (25) 3/2 X (243) 3/5 (16) 5/4 X (8) 4/3 (ii) 16 X 2 n+1 - 4 X 2 n 16 X 2 n+2 - 2 X 2 n+2
Answer
12. Assuming that x, y are positive real numbers, simplify each of the following:

(i) x -2 y 3 (ii) x -2/3 y -1/2 2 (iii) x -3 5 (iv) x -2/3 y 4 y 4

(v) 3 xy 2 x 2y (vi) 4 3 x 2
Answer
13. Identify √45 as rational number or irrational number.
Answer
14. Prove that √3 - √2 is an irrational number.
Answer
15. Write three numbers whose decimal expansions are non-terminating non recurring.
Answer
16. Give examples of two irrational numbers, the product of which is:

(i) a rational number (ii) an irrational number.
Answer
17. Find a rational number between 2 and 1.
Answer
18. Express 0.999999... in the form p/q, where p and q are integers and q 0
Answer
19. Find two rational numbers between 0.23332333233332 and 0.2525525552555-52
Answer
20. Simplify each of the following, removing radical signs and negative indices wherever they occur:

(i) (√4)-3 (ii) (√5)-3 (√2)-3 (iii) 1/ 3√4-5

(iv) (25)-1/3 x 3√16 (v) (3√8)-1/2 (vi) (√4)-7 (√2)-5
Answer
21. Express 0.001as a fraction in the simplest form.
Answer
22. Insert 100 rational numbers between -3/13 and 9/13.
Answer
23. Evaluate each of the following removing radical signs and negative indices wherever they occur:

(i) (64)1/3 (ii) (125)-1/3[NCERT] (iii) (27) - 2/3 (iv) (64/25)-3/2
Answer
24. Express each of the following decimals in the form p/q :
(i) 0.4 (ii) 0.2 (iii) 0.3
(iv)0.4 (v) 0.5 (vi)0.6
Answer
25. Represent 5/3 and -5/3 on the number line.
Answer
26. Examine whether the following numbers are rational or irrational:

(i) (√2 + 2)2 (ii) (5 + √5)(5 - √5) (iii) 6/ 2√3
Answer
27. Find one irrational number between the number a and b given below

a = 0.1111... = 0.1 and b = 0.1101
Answer
28. Find a rational number between - 2 and 6.
Answer
29. Express each of the following mixed recurring decimals in the form p/q. (i)4.32(ii)15.712
Answer
30. Find three different irrational numbers between the rational numbers 5/7 and 9/11.
Answer
31. Express each of the following numbers in the form p/q.
(i) 15.75 0 (ii) 8.0025 (iii) -24.6875
Answer
32. Find two irrational numbers lying between √2 and √3.
Answer
33. Find three rational numbers between -2 and 5.
Answer
34. Represent 8/5 and -8/5 on the the number line.
Answer
35. Find two irrational numbers between 0.12 and 0.13
Answer
36. Express each of the following numbers in the form p/q.
(i) 0.15 (ii) 0.675 (iii) 0.00026
Answer
37. Express each of the following decimals in the form p/q.
(i) 0.35 (ii)  0.0.585
Answer
38. Insert 10 rational numbers betwveen -3/11 and 8/11.
Answer
39. Show that 0.2353535... = 0.235 can be expressed in the form p/q, where p and q are integers and q 0.
Answer
40. Insert a rational and irrational number between 2 and 3.
Answer
41. Prove that √n is not a rational number, if n is not a perfect square.
Answer
42.

Show that 1.272727 = 1.27 can be expressed in the form p/q , where p and q are integers and q ≠0.


Answer
43. Find two irrational numbers between 2 and 2.5.
Answer
44. Convert the following decimal number in the form p/q.
(i) 5.2 (ii) 2343
Answer
45. Express the following decimals in the form p/q.
(i)0.32 (ii) 0.123 (iii) 0.00352
Answer
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