Class 9 Number Systems Worksheet

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Curriculum note: 'Number System' is a unit in the CBSE Class 9 Mathematics syllabus for 2026-27 (published by CBSE in April 2026, per secondary sources we checked). We could not confirm exactly which sub-topics, such as irrational numbers and surds, appear in the 2026-27 syllabus, so please check the official CBSE syllabus and your textbook before relying on this quiz for exam preparation.

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Class 9 Number Systems – Practice Worksheet

Name:

Date:

Marks: / 10

Instructions: Answer all 10 questions. Circle the correct option and show your working in the space given.

Which of these numbers is irrational?
- (A) 0.25
- (B) 4/5
- (C) √9
- (D) √2
Working:
Answer:
Which of these is a rational number between 1 and 2?
- (A) √5
- (B) 3/2
- (C) π
- (D) √3
Working:
Answer:
Write 0.333... (3 repeating) as a fraction.
- (A) 3/10
- (B) 33/100
- (C) 1/3
- (D) 1/30
Working:
Answer:
The number √16 is:
- (A) A rational number
- (B) An irrational number
- (C) Not a real number
- (D) A negative number
Working:
Answer:
The decimal expansion of 7/8 is:
- (A) Non-terminating and repeating
- (B) Non-terminating and non-repeating
- (C) Not possible to find
- (D) Terminating
Working:
Answer:
What is (2 + √3)(2 − √3)?
- (A) 7
- (B) 4
- (C) 1
- (D) 2 − 3√3
Working:
Answer:
Rationalise the denominator of 1/√2.
- (A) 1/2
- (B) √2/2
- (C) √2
- (D) 2√2
Working:
Answer:
Simplify: 2³ × 2⁴
- (A) 2¹²
- (B) 4⁷
- (C) 2¹
- (D) 2⁷
Working:
Answer:
What is the value of 27^(1/3)?
- (A) 3
- (B) 9
- (C) 81
- (D) 1/3
Working:
Answer:
Which of these numbers lies between 3 and 4?
- (A) √5
- (B) √20
- (C) √10
- (D) √16
Working:
Answer:

Original questions by LearnWise Practice Hub.

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Class 9 Number Systems – Answer Key

Answer: (D) √2
√9 = 3, 0.25 = 1/4 and 4/5 are all rational. √2 cannot be written as p/q, so it is irrational.
Answer: (B) 3/2
3/2 = 1.5 is rational and lies between 1 and 2. √5 ≈ 2.24 is outside, π ≈ 3.14 is outside, and √3 is irrational.
Answer: (C) 1/3
Let x = 0.333... Then 10x = 3.333... Subtract: 9x = 3, so x = 3/9 = 1/3.
Answer: (A) A rational number
√16 = 4, which is an integer and so can be written as 4/1. It is rational.
Answer: (D) Terminating
Dividing 7 by 8 gives 0.875 exactly, so the expansion ends. It is terminating.
Answer: (C) 1
Use (a + b)(a − b) = a² − b². Here 2² − (√3)² = 4 − 3 = 1.
Answer: (B) √2/2
Multiply top and bottom by √2: (1 × √2)/(√2 × √2) = √2/2.
Answer: (D) 2⁷
When multiplying powers with the same base, add the exponents: 2³ × 2⁴ = 2^(3+4) = 2⁷.
Answer: (A) 3
27^(1/3) is the cube root of 27. Since 3 × 3 × 3 = 27, the answer is 3.
Answer: (C) √10
3² = 9 and 4² = 16, so a number between 3 and 4 has a square between 9 and 16. √10 fits; √5 < 3, √20 > 4 and √16 = 4.

Class 9 Number Systems Worksheet

Class 9 Number Systems – Answer Key

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