We have included 30 MCQ questions for class 9 chapter 1 Chapter 1 Number System. Like 3/4, which is a rational number behave predictably with neat decimal endings. But numbers that are irrational like √2, are endless with unpredictable decimals.
CBSE Class 9th Maths Important MCQs with Answers from Chapter 1 – Number System
Question 1: Which correct chain shows how the standard number sets are nested?
a) Q ⊂ Z ⊂ W ⊂ N ⊂ R
b) N ⊂ W ⊂ Z ⊂ Q ⊂ R
c) R ⊂ Q ⊂ Z ⊂ W ⊂ N
d) W ⊂ N ⊂ Z ⊂ Q ⊂ R
Answer:
b) N ⊂ W ⊂ Z ⊂ Q ⊂ R
Question 2: Which of the following is irrational?
a) √50/5
b) (√3)²
c) π/π
d) √49
Answer:
a) √50/5
Question 3: Which statement about the decimal expansion of a rational number is always true?
a) It always terminates
b) It always repeats with period 1
c) It terminates or eventually repeats
d) It neither terminates nor repeats
Answer:
c) It terminates or eventually repeats
Question 4: How many rational numbers lie strictly between 3 and 4?
a) None
b) Exactly one
c) Finitely many
d) Infinitely many
Answer:
d) Infinitely many
Question 5: Which method always gives a rational number strictly between two rational numbers r and s (r ≠ s)?
a) r − s
b) rs
c) (r + s)/2
d) r/s
Answer:
c) (r + s)/2
Question 6: Which statement is always true for a non-zero rational number r and an irrational number x?
a) r + x is rational
b) r − x is rational
c) rx is irrational
d) x/r is rational
Answer:
c) rx is irrational
Question 7: Which of the following decimals is rational?
a) 0.142857142857…
b) 0.101001000100001…
c) 0.123456789101112…
d) 0.10110111011110…
Answer:
a) 0.142857142857…
Question 8: Which fraction, in lowest terms, has a terminating decimal expansion?
a) 13/40
b) 7/30
c) 11/24
d) 29/54
Answer:
a) 13/40
Question 9: After reducing p/q to lowest terms, the decimal expansion of p/q terminates if and only if q has which form?
a) 2m3n
b) 2m5n
c) 3m5n
d) 2m3n5k
Answer:
b) 2m5n
Question 10: The rational number 17/(2³·5²) has a terminating decimal with how many places?
a) 2
b) 3
c) 5
d) 7
Answer:
b) 3
Question 11: Which fraction equals 0.6̅ (0.666…)?
a) 3/4
b) 2/3
c) 5/9
d) 7/12
Answer:
b) 2/3
Question 12: Which fraction equals 0.47̅ (0.474747…)?
a) 47/90
b) 47/99
c) 47/900
d) 47/909
Answer:
b) 47/99
Question 13: Which fraction equals 0.001001001… ?
a) 1/9
b) 1/90
c) 1/99
d) 1/999
Answer:
d) 1/999
Question 14: Which statement about 0.9999… is correct?
a) It is less than 1 by 0.0001
b) It is exactly equal to 1
c) It is greater than 1 by 0.000…1
d) It is irrational
Answer:
b) It is exactly equal to 1
Question 15: What is the length of the repeating block in the decimal expansion of 1/7?
a) 3
b) 4
c) 6
d) 7
Answer:
c) 6
Question 16: For a positive integer n, when is √n rational?
a) Only when n is prime
b) Only when n is even
c) Exactly when n is a perfect square
d) Never
Answer:
c) Exactly when n is a perfect square
Question 17: To construct √13 on the number line using a right triangle, which pair of perpendicular legs works?
a) 1 and 13
b) 3 and 4
c) 5 and 5
d) 2 and 3
Answer:
d) 2 and 3
Question 18: Which statement is always true for a rational number r and an irrational number x?
a) r + x is irrational
b) r − x is rational
c) rx is rational
d) x/r is rational
Answer:
a) r + x is irrational
Question 19: Between any two distinct irrational numbers, which of the following holds?
a) No rational number exists
b) Exactly one rational number exists
c) Infinitely many rational and infinitely many irrational numbers exist
d) Only irrational numbers exist
Answer:
c) Infinitely many rational and infinitely many irrational numbers exist
Question 20: Which of the following is rational?
a) √2 + √8
b) √2 · √8
c) √5 + √7
d) √3 − √2
Answer:
b) √2 · √8
Question 21: What is 1/(√2 + √3) after rationalising the denominator?
a) √2 + √3
b) √3 − √2
c) (√2 − √3)/(2 − 3)
d) (√3 + √2)/(3 + 2)
Answer:
b) √3 − √2
Question 22: What is (√5 + √3)(√5 − √3)?
a) 2√15
b) 8
c) 2
d) 5 + 3
Answer:
c) 2
Question 23: Which fraction (in lowest terms) has a non-terminating repeating decimal expansion?
a) 7/125
b) 23/18
c) 19/160
d) 121/2³·5²
Answer:
b) 23/18
Question 24: What is (21/3)(22/3) equal to?
a) 21/3
b) 2
c) 22/3
d) 2/3
Answer:
b) 2
Question 25: For a > 0 and integers m, n (n > 0), what does am/n mean?
a) (an)m
b) n√(am)
c) m√(an)
d) (n√a)m
Answer:
b) n√(am)
Question 26: What is the value of 272/3?
a) 6
b) 7
c) 9
d) 3
Answer:
c) 9
Question 27: What is (53/2)/(51/2) equal to?
a) 5
b) 5²
c) 1/5
d) √5
Answer:
a) 5
Question 28: Which simplification is correct?
a) √3 · √12 = √36 = 6
b) √3 · √12 = √(3 + 12) = √15
c) √3 + √12 = √15
d) √12/√3 = √15
Answer:
a) √3 · √12 = √36 = 6
Question 29: What is (2√3)/(√12) equal to?
a) √2
b) 1
c) √3
d) 2
Answer:
b) 1
Question 30: The rationalised form of 5/(√3 − √5) is which of the following?
a) −(5/2)(√3 + √5)
b) (5/8)(√3 + √5)
c) (5/2)(√5 − √3)
d) (√3 + √5)/5
Answer:
a) −(5/2)(√3 + √5)
Question 31: Which statement about closure is correct for rational numbers Q?
a) Q is closed under division, including division by 0
b) Q is not closed under addition
c) Q is closed under addition, subtraction, multiplication, and division by any non-zero rational
d) Q is not closed under multiplication
Answer:
c) Q is closed under addition, subtraction, multiplication, and division by any non-zero rational
Question 32: Which of the following must be irrational?
a) √2 + √3
b) √2 − √2
c) √9 + √16
d) (√5)² − 1
Answer:
a) √2 + √3
Question 33: What is (√12 + √27)/√3 equal to?
a) 3
b) 4
c) 5
d) 6
Answer:
c) 5
Question 34: What is the fractional form of 0.23̅7 (that is, 0.237777…)?
a) 107/450
b) 237/999
c) 23/90
d) 213/900
Answer:
a) 107/450
Question 35: If p is a prime other than 2 or 5, what type of decimal expansion does 1/p have?
a) Terminating
b) Non-terminating non-repeating
c) Non-terminating repeating
d) Finite with exactly p digits
Answer:
c) Non-terminating repeating
Fill in the blanks on Number Systems for Class 9 Maths
1. The collection of natural numbers is denoted by the symbol ___.
Answer:
N
2. The collection of whole numbers is denoted by the symbol ___.
Answer:
W
3. The collection of all integers is denoted by the symbol ___.
Answer:
Z
4. The collection of rational numbers is denoted by the symbol ___.
Answer:
Q
5. A rational number is of the form p/q, where p and q are integers and q ≠ ___.
Answer:
0
6. Every integer is a ___ number.
Answer:
rational
7. Every rational number can be expressed either as a terminating decimal or a ___ decimal.
Answer:
non-terminating recurring
8. The decimal expansion of an irrational number is always ___ and ___.
Answer:
non-terminating, non-recurring
9. The square root of 2 was proved to be ___ by the Pythagoreans.
Answer:
irrational
10. The collection of all rational and irrational numbers together is called ___ numbers.
Answer:
real
11. The real number line represents every ___ number and every point on it corresponds to a real number.
Answer:
real
12. The decimal expansion of 7/8 is ___.
Answer:
0.875
13. The decimal expansion of 1/7 is ___.
Answer:
0.142857…
14. The sum or difference of a rational number and an irrational number is always ___.
Answer:
irrational
15. The product or quotient of a non-zero rational number and an irrational number is always ___.
Answer:
irrational
16. To rationalise 1/√2, we multiply numerator and denominator by ___.
Answer:
√2
17. The symbol used in expressions like √2 or ∛8 is called the ___ sign.
Answer:
radical
18. The value of 5th root of 243 is ___.
Answer:
3
19. According to the law of exponents, am × an = ___.
Answer:
am+n
20. The decimal expansion of π is ___.
Answer:
non-terminating and non-recurring
