Number System Class 9 in One Shot πŸ”₯ | Class 9 Maths Chapter 1 Complete Lecture | Shobhit Nirwan

Shobhit Nirwan - 9th・2 minutes read

The first chapter of the ninth class delves into the Number system, detailing real, rational, and irrational numbers, aiming for students to achieve 100 marks in Math. The text emphasizes the distinction between rational and irrational numbers, provides examples, and offers formulas for finding rational numbers between two values.

Insights

  • The chapter on Number System in the ninth class covers real numbers, rational numbers, and irrational numbers, emphasizing their definitions and distinctions.
  • The text provides detailed explanations on decimals, rational and irrational numbers, highlighting the significance of understanding their properties and differences.
  • Practical exercises and formulas are introduced to help students find rational and irrational numbers between given values, reinforcing mathematical problem-solving skills and critical thinking.

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Recent questions

  • What is the importance of understanding the Number system?

    Understanding the Number system is crucial for class ninth students as it forms the foundation for mathematical concepts. It covers real numbers, rational numbers, irrational numbers, and their properties, which are fundamental in solving mathematical problems. Mastery of the Number system ensures students can confidently tackle questions from various textbooks and exams, leading to academic success in mathematics.

  • How are rational numbers defined in the Number system?

    Rational numbers are defined as numbers in the form of p/q, where q is not equal to 0, and p and q belong to integers. This definition distinguishes rational numbers from other types like natural and irrational numbers. Understanding rational numbers is essential as they play a significant role in mathematical calculations and problem-solving, forming a critical part of the Number system.

  • What is the significance of decimals in the Number system?

    Decimals are a crucial aspect of the Number system as they represent fractional parts of numbers. Understanding decimals is essential for precise calculations, especially when dealing with real-world measurements and values. The concept of decimals helps students grasp the idea of fractions, percentages, and the relationship between different numerical representations, enhancing their mathematical skills.

  • How are irrational numbers differentiated in the Number system?

    Irrational numbers are distinguished in the Number system based on their decimal representations. Unlike rational numbers, irrational numbers have non-repeating and non-terminating decimals. Identifying irrational numbers is important as they exist alongside rational numbers, expanding the understanding of numerical concepts and providing a comprehensive view of the Number system.

  • What is the practical application of Pythagoras' theorem in the Number system?

    Pythagoras' theorem is a fundamental concept in the Number system used to calculate the hypotenuse of a right-angled triangle. By understanding this theorem, students can determine the relationship between the sides of a triangle and apply it to solve geometric problems. Pythagoras' theorem showcases the practical application of mathematical principles in real-world scenarios, emphasizing the relevance of geometry within the Number system.

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Summary

00:00

"Number System: Key Concepts for Class Nine"

  • The first chapter of the ninth class is about the Number system, a crucial topic for class ninth students.
  • The chapter is detailed, easy, and lengthy, promising a thorough discussion in the lecture.
  • The instructor encourages students to engage fully in the lecture, promising a transformative learning experience.
  • The lecture guarantees that students will confidently solve questions from NCRT, RD, and RS after completion.
  • The aim is for students to achieve 100 marks in Math, emphasizing dedication and focus.
  • The chapter delves into the concept of real numbers, rational numbers, and irrational numbers.
  • Natural numbers are explained as those that come naturally while counting, starting from 1, 2, 3, and so on.
  • Whole numbers are introduced by adding zero to natural numbers, representing a complete set of numbers.
  • Negative numbers are discussed as those below zero, represented as -1, -2, -3, and so on.
  • Rational numbers are defined as numbers in the form of p/q, where q is not equal to 0, and p and q belong to integers.

13:24

Understanding Decimals and Rational Numbers

  • The text discusses the termination of numbers and the concept of decimals.
  • It explains the termination of numbers like 1.5, 0.2, and 0.
  • The text delves into the division of numbers like 22/7 and the resulting values.
  • It explores the concept of Pi, mentioning its approximate value of 3.14.
  • The text distinguishes between rational and irrational numbers based on repeating or terminating decimals.
  • It emphasizes the importance of understanding decimals after the decimal point.
  • The text provides examples of rational numbers like 22/7 and irrational numbers like Pi.
  • It discusses the exact value of Pi as 3.14 and the misconception of 22/7 being its exact value.
  • The text presents a multiple-choice question scenario involving Pi and rational numbers.
  • It concludes with a discussion on true or false statements regarding whole numbers, natural numbers, integers, and rational numbers.

27:41

Understanding Rational Numbers and Decimal Expansion

  • Numbers are not integers, every integer is rational.
  • Rational numbers are of the form p/q, which won't be an integer.
  • Revision within 24 hours of a lecture is crucial.
  • Natural numbers are whole numbers, including 0, 1, 2, etc.
  • Every integer is a whole number, including negatives.
  • Decimal expansion of 1/7 is 0.142857.
  • Predicting the decimal expansion of 4/7 without division is 0.571428.
  • Finding rational numbers between two rational numbers involves the formula a + b / 2.
  • To find five rational numbers between 1/7 and 2/7, use the formula a + b / 2.
  • To find 50 rational numbers between two rational numbers, increment by the same value each time.

40:17

"Rational Numbers: Simplify, Convert, and Prove"

  • Write down the five best choices and publish them.
  • Extract rational numbers between 70/10 and 10.
  • Choose Annie to simplify the process.
  • Determine 20 times 10 and 15 rational numbers between 60/2.
  • Multiply and divide to convert 4/6 back to 2/3.
  • Multiply and divide by 100 to find 70 rational numbers.
  • Convert 5 to the p/q form by multiplying by 10.
  • Convert 3.2 to 16/5 in the p/q form.
  • Prove that 3.142678 is a rational number by removing zeros.
  • Express 0.3333... in the p/q form by considering x as the repeating decimal.

54:48

Decimals, Equations, and X Values Calculations

  • 10 went to two and 100 went to three
  • 1000 becomes four, then 10000 becomes four
  • Multiplying by 10 on both sides
  • Moving decimals forward by multiplying by 10
  • Expressing decimals in different forms
  • Subtraction of equations to find x values
  • Calculating x values based on equations
  • Converting decimals into p bar k form
  • Considering bars immediately after decimals as x
  • Multiplying both sides by 100 when bar is on two and then subtracting equations

01:09:11

Irrational Numbers and Their Properties

  • Positive integers result in irrational numbers when square rooted, such as √1, √2, √3, √4, √5, √6, √7.
  • Perfect squares, like the square root of 4, are not irrational.
  • The square root of any perfect square is not irrational.
  • The cube of 2 is 8, and the cube of 3 is 27, resulting in irrational numbers.
  • The negative of an irrational number remains irrational, such as -√2, -√3, -√7.
  • The sum, difference, product, and division of rational and irrational numbers can result in irrational numbers.
  • To find irrational numbers between two rational numbers, use the formula r = √(a + b) / 2.
  • Two irrational numbers between 4 and 5 can be found by considering non-repeating, non-terminating decimals.
  • Five irrational numbers between 5 and 6 can be determined using the same method.
  • To find irrational numbers between two irrational numbers, consider the square roots of the given numbers and find values in between.

01:23:29

Discovering Irrational Numbers Between 12 and 13

  • Insert two irrational numbers between 12 and 13, without specifying the values.
  • Emphasize the simplicity of the task, encouraging self-discovery.
  • Highlight the importance of not pausing while solving the problem.
  • Mention the significance of avoiding numbers larger than one between 0 and 1.
  • Suggest looking for numbers between 0.12 and 0.13.
  • Specify the range for the two irrational numbers to be between 0.12 and 0.13.
  • Explain the process of representing irrational numbers on a number line.
  • Introduce Pythagoras' theorem for calculating hypotenuse.
  • Detail the method for determining base and perpendicular to achieve specific hypotenuse values.
  • Provide a systematic approach for representing various square roots on a number line.

01:36:36

"Understanding Powers and Roots in Mathematics"

  • To find the base for √50, the base should be 49.
  • The base for √50 is 7, with a perpendicular of 1.
  • The hypotenuse for √50 is automatically calculated.
  • To draw a perpendicular, the base and perpendicular are needed.
  • When the base is 7 and the perpendicular is 1, the hypotenuse is √50.
  • Instructions on using a compass to measure and bring down √50 are provided.
  • Mathematical rules for same base powers are explained.
  • The cube root of 3 to the power of 4 is detailed.
  • Various mathematical identities and examples are shared.
  • Practical questions involving powers and roots are presented for practice.

01:49:38

Solving Math Problems with Powers and Bases

  • If 2 times 5 equals 32 to the power of 2, with 5 to the power of 2 being 1/5 saved.
  • A brain-teasing question is posed, requiring careful consideration and a 5-minute pause.
  • All identities are mentioned once, to be applied and solved in three to four slides.
  • The concept of same base and different powers is explained, with the rule of adding powers when multiplying.
  • LCM is used to simplify expressions, with detailed steps on how to take LCM.
  • The process of simplifying expressions involving different bases and powers is elaborated on.
  • The rule that anything to the power of 0 equals 1 is emphasized.
  • The importance of understanding and memorizing formulas is highlighted for solving complex problems.
  • Rationalization is explained, detailing the process of multiplying and dividing to simplify expressions with roots.
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