Number Systems (Class 9 Mathematics)
Number systems encompass natural numbers, whole numbers, integers, rational, and irrational numbers. Understanding the properties and representation of the
TL;DR: Number systems encompass natural numbers, whole numbers, integers, rational, and irrational numbers. Understanding the properties and representation o…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Number systems encompass natural numbers, whole numbers, integers, rational, and irrational numbers. Understanding the properties and representation of the
Number Systems MCQs with Answers & Explanations
Q1. Which of the following is a whole number but not a natural number?
- 1
- 2
- 0 ✓ (correct)
- -1
Explanation: Whole numbers are {0, 1, 2, 3, ...}, while natural numbers are {1, 2, 3, ...}. Zero is a whole number but not a natural number.
Q2. A rational number can be expressed as:
- p ÷ q where q = 0
- √(p/q)
- p × q
- p/q where p and q are integers and q ≠ 0 ✓ (correct)
Explanation: By definition, a rational number is a number that can be expressed as p/q where p and q are integers and q ≠ 0.
Q3. √9 is:
- Rational ✓ (correct)
- Neither rational nor irrational
- Irrational
- Not a real number
Explanation: √9 = 3, which is an integer and therefore a rational number.
Q4. Which of the following is an irrational number?
- √9
- √10 ✓ (correct)
- √4
- √16
Explanation: √10 cannot be expressed as a ratio of integers and has a non-terminating, non-repeating decimal expansion.
Q5. The decimal representation of 1/6 is:
- 0.1̄6̄
- 0.166
- 0.1666... ✓ (correct)
- 0.16
Explanation: 1/6 = 0.1666... which is a non-terminating, repeating decimal (0.1̄6̄).
Q6. On a number line, integers are:
- Not equally spaced
- Only on one side of zero
- Only positive numbers
- Symmetrically placed about zero ✓ (correct)
Explanation: Integers {..., -2, -1, 0, 1, 2, ...} are symmetrically placed about zero and equally spaced on a number line.
Q7. Which set of numbers is closed under subtraction?
- Integers ✓ (correct)
- Natural numbers
- Rational numbers
- Whole numbers
Explanation: Integers are closed under subtraction; subtracting any two integers always gives an integer.
Q8. The set {-2, -1, 0, 1, 2} represents:
- Whole numbers
- Integers ✓ (correct)
- Natural numbers
- Rational numbers
Explanation: This set contains negative numbers, zero, and positive numbers, which together form a subset of integers.
Q9. Which of the following is NOT a real number?
- π
- √2
- √-1 ✓ (correct)
- 0
Explanation: √-1 = i is an imaginary number, not a real number. Real numbers include rationals and irrationals but exclude imaginary numbers.
Q10. The decimal expansion of 22/7 is:
- 3.1̄4̄2̄8̄5̄7̄
- Non-terminating and non-repeating
- 3.14
- 3.142857142857... ✓ (correct)
Explanation: 22/7 = 3.142857142857..., a non-terminating repeating decimal with period 142857.
Frequently Asked Questions
How are rational and irrational numbers different?
Rational numbers can be expressed as p/q (where p, q are integers and q ≠ 0) and have terminating or repeating decimal expansions. Irrational numbers cannot be expressed as fractions and have non-terminating, non-repeating decimal expansions.
What is the difference between natural numbers and whole numbers?
Natural numbers start from 1 and include {1, 2, 3, ...}. Whole numbers include zero and all natural numbers: {0, 1, 2, 3, ...}. The main difference is that whole numbers include zero.
More Class 9 Mathematics MCQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →