CBSE Important Questions for Class 9 Maths Number Systems

Find the important questions for Class 9 Maths Chapter 1- Number System here. These practice questions help students understand core concepts better and prepare effectively for CBSE Class 9 exams. By solving them, students can get familiar with the types of questions asked in the final exams and build confidence to score well.

Also Check:

• Important Questions for Class 9 with solutions
• Important Questions for Class 9 Maths Quadrilaterals with solutions

Important Questions on Number System Class 9 With Answers

The important questions for Class 9 Maths Chapter 1 – Number Systems are designed to strengthen your understanding of key concepts. These carefully chosen questions cover all major topics and help improve your problem-solving skills. Regular practice will enhance your conceptual clarity and boost your confidence for exams. Whether you're preparing for unit tests or the final CBSE board exam 2026, these questions are a great resource to master the chapter.

Number System Important Questions For Class 9 Chapter 1

The important Number System questions given below for Class 9 students will help them explore different types of problems and strengthen their problem-solving skills.

Q. Find five rational numbers between 1 and 2.

Solutions: To find rational numbers between 1 and 2, we can divide the difference into smaller equal parts.

Let’s express them with denominator 10 for simplicity.

Between 1 (=10/10) and 2 (=20/10), the rational numbers are:

11/10, 12/10, 13/10, 14/10, and 15/10.

Answer: 11/10, 12/10, 13/10, 14/10, 15/10

These are fractions between 1 and 2, and all are rational because they can be expressed in the form p/q.

Q. Find five rational numbers between 3/5 and 4/5.

Solution: Let’s make the denominators larger so that we can find numbers in between.

Multiply both by 10 to make the denominator 50:

3/5 = 30/50 and 4/5 = 40/50.

Now the numbers between them are:

31/50, 32/50, 33/50, 34/50, and 35/50.

Answer: 31/50, 32/50, 33/50, 34/50, 35/50

All these fractions lie between 3/5 and 4/5 and are rational (both numerator and denominator are integers).

Q. Are the square roots of all positive integers irrational? If not, give an example.

Solution: No, the square roots of all positive integers are not irrational.

If the number is a perfect square, its square root is rational.

Example: √4 = 2 (which is rational because it can be expressed as 2/1).

Answer: No, not all are irrational. Example: √4 = 2 is rational.

Square roots of perfect squares (like 1, 4, 9, 16, 25, etc.) are rational numbers.

Q. Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Solution: Let’s first convert them into decimals for better understanding:

5/7 ≈ 0.714 and 9/11 ≈ 0.818.

Now, we need three irrational numbers between 0.714 and 0.818.

Irrational numbers are non-repeating, non-terminating decimals.

Examples:

0.72√2 ≈ 0.72 × 1.414 ≈ 1.018 (too high, adjust)

Better examples in the range can be:

• √0.52 ≈ 0.7211
• √0.53 ≈ 0.7280
• √0.67 ≈ 0.8185 (slightly above 0.818 but acceptable with rounding)

So we can slightly adjust and take:

√0.52, √0.53, √0.54

Answer: √0.52, √0.53, √0.54

These numbers are irrational because the square roots of non-perfect squares are irrational, and they fall between 5/7 and 9/11.

Q. Add 2√2+ 5√3 and √2 – 3√3.

Solution: (2√2 + 5√3) + (√2 – 3√3)

= 2√2 + 5√3 + √2 – 3√3

= (2 + 1)√2 + (5 – 3)√3

= 3√2 + 2√3

Q. Rationalise the denominator of 1/[7+3√3].

Solution: 1/(7 + 3√3)

By rationalizing the denominator,

= [1/(7 + 3√3)] [(7 – 3√3)/(7 – 3√3)]

= (7 – 3√3)/[(7)2 – (3√3)2]

= (7 – 3√3)/(49 – 27)

= (7 – 3√3)/22

Q. Simplify: (√3+√7) (√3-√7).

Solution: (√3 + √7)(√3 – √7)

Using the identity (a + b)(a – b) = a2 – b2,

(√3 + √7)(√3 – √7) = (√3)2 – (√7)2

= 3 – 7

= -4

Q. Simplify:

(i) 7^2/3.7^1/5

(ii) 10^1/2/10^1/4

Solution:

(i) 7^2/3.7^1/5

Bases are equal, so add the powers.

7^{(2/3 + 1/5)}

= 7^{(10 + 3)/15}

= 7^13/15

(ii) 10^1/2/10^1/4

Bases are equal, so subtract the powers.

= 10 ^{(1/2 – 1/4)}

= 10^1/4

Q. What is the product of a rational and an irrational number?

a) Always an integer

b) Always a rational number

c) Always an irrational number

d) Sometimes rational and sometimes irrational

Solutions: When you multiply a rational number by an irrational number, the result is always irrational.

For example, 2 is a rational number and √3 is irrational. Therefore, their product, 2√3, is an irrational number.

Correct answer: Option (c)

Q. What is the value of (256)^0.16 X (256)^0.09?

a) 4

b) 16

c) 64

d) 256.25

Solution:  (256)^0.16 x (256)^0.09 = (256)^{(0.16 + 0.09)}

= (256)^0.25

= (256)^(25/100)

= (256)^(1/4)

= (4⁴)^(1/4)

= 4^4(1/4)

= 4

Correct answer: Option (a)

Important Questions for Class 9 Maths Chapter 1 - Free PDF Download

Class 9 is an important stage in your academic journey as it prepares you for your Class 10 board exams. This is the time to focus on building strong concepts and good study habits. Understanding topics like the Number System is very important because these concepts are used later in subjects like Physics, Electronics, and higher-level Maths. So, it’s best to strengthen your foundation in Maths with these Important Questions for Class 9 Chapter 1.

Infinity Learn offers a free PDF download of important questions for Class 9 Maths Chapter 1 to help students prepare as per the latest CBSE syllabus 2026. Since CBSE follows a specific pattern, these questions are designed accordingly to give you a clear idea of how to approach exams. The PDF includes detailed explanations and examples to help you understand each concept easily. It’s especially useful for students who find Maths difficult, as it provides step-by-step solutions to strengthen their understanding and confidence in the Number System chapter.

Benefits of Important Questions for Class 9 Maths Number Systems

Number System Class 9 Important Questions PDF is prepared by expert teachers and is available free of cost. Students can also practice extra questions to strengthen their understanding of the Number System chapter. These questions are especially helpful for those who find Maths difficult or less interesting. All questions follow the latest CBSE guidelines and exam pattern, so students don’t need to search anywhere else.

Why You Should Refer to Class 9 Maths Chapter 1 Important Questions

• The important questions PDF is free to access and download.
• These questions are perfect for exam preparation and homework revision, helping students clear their concepts.
• The PDF format makes it easy to download and study offline, saving time and effort.
• Students can print the PDFs to study comfortably without depending on screens.
• All questions and answers strictly follow CBSE standards, helping students understand the exam pattern.

In the Class 9 Maths paper (100 marks), 20 marks are for internal assessment, and 80 marks are for the written exam. Chapter 1 – Number System carries around 8 marks, making it an important chapter to focus on.

Other Important Related Links for CBSE Class 9 Maths