Practice Essential Number System Questions for Class 9 Maths (2025-26)
FAQs on Number System Worksheets for CBSE Class 9 Maths – Free PDF Solutions
1. What are the most frequently asked types of important questions from Chapter 1, Number System, for the Class 9 final exam?
For the CBSE Class 9 exam for the year 2025-26, the important questions from Number Systems are typically structured by marks as follows:
2-Mark Questions: Finding a set of rational numbers between two given numbers, or simplifying expressions using the laws of exponents.
3-Mark Questions: Representing irrational numbers like √3 or √5 on the number line, and converting recurring decimals into the p/q form.
4/5-Mark Questions (HOTS): These often involve complex rationalisation or multi-step simplification problems that combine several laws of exponents.
2. How should I answer a question on representing an irrational number like √9.3 on the number line to get full marks?
To secure full marks for representing a decimal root, you must show the geometric construction steps clearly. For √9.3, the key steps are: draw a line segment of 9.3 units, extend it by 1 unit, find the midpoint to draw a semicircle, and then draw a perpendicular from the end of the 9.3 unit mark to the semicircle. The length of this perpendicular is exactly √9.3, which you then project onto the number line. Clearly labelling all points (A, B, C, etc.) and using a compass and ruler accurately is crucial.
3. Which types of rationalisation questions are considered most important for exams?
The most important and expected questions on rationalisation involve denominators of the form 1/(√a ± √b) or 1/(a ± √b). To solve these, you must multiply the numerator and denominator by the conjugate of the denominator. This process tests your ability to correctly apply the algebraic identity (x - y)(x + y) = x² - y², which is a fundamental skill for this chapter.
4. What are some expected MCQ-type questions from the Number System chapter?
Important multiple-choice questions (MCQs) for Chapter 1 often test core conceptual understanding. Expect questions such as:
Identifying an irrational number from a given set of options (e.g., √16, √8, 0.5).
A question on the nature of the decimal expansion of an irrational number, which is always non-terminating and non-recurring.
A simple calculation based on the laws of exponents, like finding the value of (64)^(1/2).
5. Are all integers rational numbers, but not all rational numbers are integers? Explain why this is a common trap in 1-mark questions.
This is a critical distinction for scoring well in objective questions. Yes, all integers are rational numbers because any integer 'z' can be expressed in the form p/q as z/1 (e.g., -5 = -5/1). However, not all rational numbers are integers. A number like 2/3 is a rational number because it is in the form p/q, but it is not an integer. Understanding this hierarchy helps avoid common mistakes in 'True/False' or 'Choose the correct statement' questions.
6. Why is rationalising the denominator considered such an important final step when solving problems with irrational numbers?
Rationalising the denominator is an essential skill in exams for two main reasons. First, it converts the number into a standard and simplified form, which is often required to be awarded full marks. Second, it makes further operations like addition or subtraction much easier by creating an integer in the denominator. An expression with an irrational root in the denominator is technically considered un-simplified in mathematics.
7. How do the laws of exponents apply to questions with rational powers, a concept frequently tested in exams?
Questions involving rational exponents are a staple of this chapter. For an expression like (81)^(3/4), you must apply the laws of exponents systematically. The key is to first express the base as a power that cancels the denominator of the exponent. For instance, 81 = 3⁴. The expression becomes (3⁴)^(3/4). Using the law (x^a)^b = x^(ab), the powers multiply to give 3³, which equals 27. Showing these steps is vital for securing marks.
8. What is the fundamental difference between a recurring decimal and a non-terminating, non-recurring decimal, and how does this impact exam questions?
The fundamental difference determines whether a number is rational or irrational, a key concept for Higher Order Thinking Skills (HOTS) questions. A number is rational if its decimal form is either terminating (e.g., 2.5) or non-terminating but recurring (e.g., 1.333...). In contrast, a number is irrational if its decimal form is both non-terminating and non-recurring (e.g., the value of π or √2). Exam questions can ask you to classify numbers or justify why a product of a rational and an irrational number is irrational, based on this principle.











