Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5 – NCERT

Understanding numbers is the first step in mastering mathematics. Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5 covers the basics of real numbers, their properties, and how they are used in various mathematical operations. This chapter helps students revise and build upon what they have already learned in earlier classes, while also introducing new concepts like irrational numbers, laws of exponents for real numbers, and representing real numbers on the number line.

Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5

Each exercise in this chapter is designed to strengthen conceptual clarity. Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5 includes problems based on rational and irrational numbers, number line representations, and operations using laws of exponents. These exercises not only improve problem-solving skills but also lay a solid foundation for algebra and higher mathematics.

Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5

Ex 1.1  Introduction to Number Systems
Ex 1.2 Irrational Numbers
Ex 1.3  Real Numbers and Their Decimal Expansions
Ex 1.4 Representing Real Numbers on the Number Line
Ex 1.5 Operations on Real Numbers

Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5

  1. What Are Irrational Numbers?

An irrational number is a number that cannot be expressed in the form p/q, where p and q are integers and q ≠ 0.

  • Decimal expansion is non-terminating and non-repeating.
  • Examples: √2, π, √3, √5

Difference between Rational and Irrational Numbers:

Rational Numbers:

  • Can be written as p/q
  • Decimal is terminating or repeating
  • Examples: 1/2, 0.75, 2.333…

Irrational Numbers:

  • Cannot be written as p/q
  • Decimal is non-terminating and non-repeating
  • Examples: √2, π

Important Points:

  • √2 = 1.414213… (Irrational)
  • 22/7 = 3.142857… (Repeating → Rational)
  • π = 3.141592… (Irrational)

NCERT Questions – Exercise 1.1

Q1: Is zero a rational number? Can you write it in the form p/q?

Answer: Yes, 0 is a rational number because it can be written as 0/1, 0/2, 0/3, etc., where denominator ≠ 0.

Q2: Find six rational numbers between 3 and 4.

Answer:
Convert to 30/10 and 40/10. Pick any six numbers between them:
31/10, 32/10, 33/10, 34/10, 35/10, 36/10
So the numbers are: 3.1, 3.2, 3.3, 3.4, 3.5, 3.6

Q3: Find five rational numbers between 3/5 and 4/5.

Answer:
Convert to same denominator:
3/5 = 30/50, 4/5 = 40/50
Now choose: 31/50, 32/50, 33/50, 34/50, 35/50

Q4: State true or false. Give reasons.

(i) Every natural number is a whole number. → True
(ii) Every integer is a whole number. → False (e.g., -1 is not a whole number)
(iii) Every rational number is a whole number. → False (e.g., 1/2 is rational but not whole)

Extra Examples:

  • Is √81 rational? → Yes, √81 = 9
  • Is 0.101001000100001… irrational? → Yes, non-repeating, non-terminating

Chapter Overview: Number Systems (Class 9)

Key Concepts to Highlight:

  • Real numbers
  • Irrational and rational numbers
  • Number line representation
  • Laws of exponents
  • Operations on real numbers

Class 9 Math Ch 1 Number System Ex 1.1 to Ex 1.5

Exercise 1.1 – Irrational Numbers

  • Define irrational numbers
  • Give examples (like √2, π, √5, etc.)
  • Difference between rational and irrational numbers
  • Show on number line: locating √2, √3, etc.
  • Real-life connection: π in circle calculations

Exercise 1.2 – Representing Real Numbers on the Number Line

  • Step-by-step construction using compass (e.g., locating √2)
  • Combine explanation + geometric activity
  • Add interactive or visual content (like animations or Canva slides)

Exercise 1.3 – Operations on Real Numbers

  • Closure, commutative, associative properties
  • Distributive law
  • Identity and inverse elements
  • Add examples and a comparison table

Exercise 1.4 – Rationalization

  • Concept of conjugates
  • How to rationalize denominator
  • Rules to follow: multiplying by conjugate
  • Practice problems with step-by-step solutions

Exercise 1.5 – Laws of Exponents for Real Numbers

  • Special cases like a0=1
  • Table summarizing laws
  • Solve tricky exponents with fractions and negative powers

General Enrichment Ideas:

  • Add chapter summary with all formulas and key points.
  • Include NCERT exemplar problems.
  • Add real-life uses of irrational numbers and exponents.
  • Include practice quiz or MCQs after each exercise.

Class-wise Solutions

Class 12:

Class 12 Physics – NCERT Solutions

Class 12 Chemistry – NCERT Solutions

Class 11:

Class 10:

Class 9:

Class 8:

Class 7:

Class 6:

Subject-wise Solutions

Physics:

Chemistry:

Biology:

Math:

Science:

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For the official Class 9 Mathematics Solutions, you can visit:

  1. NCERT Textbooks (for Class 9):
ncert resources