CONCEPT NOTES
📌 1. Number System
The number system includes different types of numbers:
- Natural numbers (N): 1, 2, 3, …
- Whole numbers (W): 0, 1, 2, 3, …
- Integers (Z): … -2, -1, 0, 1, 2 …
- Rational numbers (Q): numbers in form p/q (q ≠ 0)
- Irrational numbers: cannot be written as p/q
📌 2. Real Numbers
Real numbers include:
- Rational numbers
- Irrational numbers
👉 All numbers on number line are real numbers.
📌 3. Rational Numbers
A number is rational if it can be written as:
👉 p/q where p, q are integers and q ≠ 0
Examples:
- 1/2, -3/4, 5, 0.75
📌 4. Irrational Numbers
Numbers that cannot be written in p/q form.
Examples:
- √2, √3, √5, π
👉 Decimal expansion is non-terminating and non-repeating.
📌 5. Representation on Number Line
- All real numbers can be shown on a number line
- Rational numbers are exact points
- Irrational numbers are approximated
📌 6. Decimal Expansion
Rational numbers:
- Terminating OR repeating decimals
Example: 1/4 = 0.25
Irrational numbers:
- Non-terminating, non-repeating
Example: √2 = 1.4142…
🔹 SECTION A: MCQs (1–70)
1. Natural numbers start from:
A) 0 B) 1 C) -1 D) 2
Ans: B
2. Whole numbers include:
A) negatives B) fractions C) 0 D) decimals
Ans: C
3. Integers include:
A) fractions only B) decimals only C) positive & negative whole numbers D) only positives
Ans: C
4. Rational numbers are of form:
A) a+b B) a/b C) a-b D) a×b
Ans: B
5. Irrational number example:
A) 1/2 B) 0.5 C) √2 D) 3
Ans: C
6. √9 is:
A) irrational B) rational C) undefined D) decimal
Ans: B
7. π is:
A) rational B) integer C) irrational D) whole number
Ans: C
8. Decimal of rational number is:
A) non-terminating repeating
B) terminating or repeating
C) random
D) infinite non-repeating
Ans: B
9. Decimal of irrational number is:
A) terminating B) repeating C) non-terminating non-repeating D) whole
Ans: C
10. Between any two numbers there are:
A) 0 numbers B) 1 number C) finite numbers D) infinite numbers
Ans: D
11. Real numbers include:
A) only integers B) only rational C) rational + irrational D) only fractions
Ans: C
12. 0 is a:
A) natural number B) whole number C) irrational number D) negative number
Ans: B
13. √2 is:
A) rational B) integer C) irrational D) whole
Ans: C
14. 3/4 is:
A) irrational B) rational C) integer D) whole
Ans: B
15. Every integer is:
A) rational B) irrational C) decimal D) fraction
Ans: A
16. Number line represents:
A) only integers B) only fractions C) real numbers D) only natural numbers
Ans: C
17. Rational number 1/2 in decimal is:
A) 0.25 B) 0.5 C) 2 D) 1
Ans: B
18. Irrational numbers cannot be written as:
A) integers B) p/q C) decimals D) roots
Ans: B
19. √4 is:
A) irrational B) rational C) undefined D) negative
Ans: B
20. 0.333… is:
A) irrational B) rational C) integer D) natural
Ans: B
SECTION B: ASSERTION–REASON (71–85)
A: Both true, R correct explanation
B: Both true, R not explanation
C: A true, R false
D: A false, R true
71. A: √2 is irrational
R: It cannot be expressed as p/q
Ans: A
72. A: Every real number is rational
R: Irrational numbers are also real
Ans: D
73. A: 0.5 is rational
R: It can be written as 1/2
Ans: A
74. A: π is rational
R: It has terminating decimal
Ans: D
75. A: Between two numbers infinite numbers exist
R: Number line is continuous
Ans: A
📊 SECTION C: NUMERICALS (86–95)
86. Convert 0.25 into fraction → ?
Ans: 1/4
87. Find √49 → ?
Ans: 7
88. Is 0.666… rational or irrational?
Ans: Rational
89. Find 3/5 in decimal → ?
Ans: 0.6
90. Is √3 rational or irrational?
Ans: Irrational
91. Between 2 and 3 how many numbers exist?
Ans: Infinite
92. Convert 1/8 into decimal → ?
Ans: 0.125
93. Is 5 an integer?
Ans: Yes
94. Is -7 a rational number?
Ans: Yes
95. Is 0 a whole number?
Ans: Yes
📄 SECTION D: VERY SHORT ANSWERS (96–100)
96. Define rational number
Ans: Number in form p/q where q ≠ 0
97. Define irrational number
Ans: Cannot be written as p/q
98. What are real numbers?
Ans: Rational + Irrational numbers
99. Give one example of irrational number
Ans: √2
100. What is number line?
Ans: A line representing real numbers