Class 9 • Maths • Chapter 1
Number Systems
True & False Quiz
Natural. Integer. Irrational. Real.
✓True
✗False
25
Questions
|
Ch.1
Chapter
|
IX
Class
Why True & False for Number Systems?
How this format sharpens your conceptual clarity
🔵 The number system is the first building block of all mathematics — every Class IX and X chapter builds on a thorough understanding of real numbers.
✅ T/F targets the hierarchy ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ, properties of irrational numbers, and laws of exponents for real numbers.
🎯 Classic trap: every rational number is real (TRUE), but not every real number is rational — √2 and π are irrational reals.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
Every natural number is a whole number.
Q 2
Zero is a natural number.
Q 3
The set of integers contains both positive and negative numbers.
Q 4
Every integer is a whole number.
Q 5
Every rational number is also a whole number.
Q 6
Irrational numbers can be represented on the number line.
Q 7
Every real number is rational.
Q 8
The decimal representation of a rational number always terminates.
Q 9
Pi (π) is a rational number.
Q 10
Whole numbers include zero.
Q 11
There is no smallest positive real number.
Q 12
Division by zero is defined.
Q 13
Rational numbers are closed under subtraction.
Q 14
The square of any real number is negative.
Q 15
Negative numbers like -5 are real numbers.
Q 16
An irrational number cannot be expressed as a fraction.
Q 17
The sum of two irrational numbers is always irrational.
Q 18
Square roots of all positive integers are irrational numbers.
Q 19
Zero is neither positive nor negative.
Q 20
Every prime number is an integer.
Q 21
Every whole number is a rational number.
Q 22
Every rational number can be converted into a decimal.
Q 23
All terminating decimals are rational.
Q 24
Negative numbers are included in the set of whole numbers.
Q 25
Between any two rational numbers there is at least one irrational number.
Key Takeaways — Number Systems
Core facts for CBSE Boards & exams
1
Number hierarchy: ℕ ⊂ W ⊂ ℤ ⊂ ℚ ⊂ ℝ (Natural ⊂ Whole ⊂ Integer ⊂ Rational ⊂ Real).
2
Rational numbers have terminating or recurring decimal expansions.
3
Irrational numbers have non-terminating, non-recurring decimal expansions (e.g. √2, π, e).
4
Between any two distinct real numbers, infinitely many real numbers exist.
5
Laws of exponents: aᵐ · aᵑ = aᵐ⁺ᵑ; (aᵐ)ᵑ = aᵐᵑ; aᵐ · bᵐ = (ab)ᵐ.
6
Rationalising the denominator: multiply numerator and denominator by the conjugate surd.