Number system Archives – Mathemafia

Class 9 Chapter 1 | All Solutions | Number System

Sunil Syal — Thu, 16 Dec 2021 06:50:19 +0000

All Mathemafia YouTube videos of Class 9 chapter 1 (Number System) are embedded on this webpage. You can watch all these videos right here in the same order as they appear in the NCERT textbook. Number system is the base of Mathematics and it is very important for students to have very good knowledge of it. In the first introductory video, Number System has been explained in detail with very easy to understand examples. you are advised to must watch the introductory video before watching any of the chapter’s example or question. Here is the list of all solved video tutorials of this chapter at one place – Examples, concepts, exercises, theorems | Class 9 Chapter 1, Number System.

This playlist covers all questions, concepts and examples of chapter 1 (Number System) of class 9, NCERT textbook. You may watch all these tutorials on YouTube by clicking the link displayed below or click a thumbnail to watch the tutorials on this webpage.

Watch complete chapter on YouTube

Example 1 and 2 Chapter 1 Class 9 | Number System | NCERT Maths

Question 1 Exercise 1.1 Class 9 | Chapter 10 | Number Systems | solution | NCERT Maths

Question 2 Exercise 1.1 Class 9 | Chapter 10 | Number Systems | solution | NCERT Maths

Question 3 Exercise 1.1 Class 9 | Chapter 10 | Number Systems | solution | NCERT Maths

Question 4 (Q4) Exercise 1.1 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Example 3 and 4 Chapter 1 Class 9 | Number System | NCERT Maths

Number System in math – Best explained with real life examples in hindi

Question 1 (Q1) Exercise 1.2 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 2 (Q2) Exercise 1.2 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 3, Activity 4 (Q3, Q4) Exercise 1.2 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Difference between Rational and Irrational numbers| Number System | Concepts explained with examples

Example 5 and 6 Chapter 1 Class 9 | Number System | NCERT Maths

Example 7, 8 and 9 Chapter 1 Class 9 | Number System | NCERT Maths

Example 10 Chapter 1 class 9 | Find an irrational no between 1/7 and 2/7| NCERT Maths | Solution

Question 1 (Q1) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 2 (Q2) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 3 (Q3) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 4 (Q4) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 5 (Q5) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 6 (Q6) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 7, 8 (Q7, Q8) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 9 (Q9) Exercise 1.3 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Example 15 Chapter 1 Class 9 | Number System | Simplify the expressions | NCERT Maths

Example 16 Chapter 1 Class 9 | Number Systems | Rationalise the denominator | NCERT Maths

Example 17, 18, and 19, Chapter 1 Class 9 | Number System | NCERT Maths

Question 1 (Q1) Exercise 1.4 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 2 (Q2) Exercise 1.4 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 3 (Q3) Exercise 1.4 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 5 (Q5) Exercise 1.4 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Example 20, Chapter 1, Class 9 | Number Systems | Simplify using Laws of Exponents | NCERT Maths

Question 1 (Q1) Exercise 1.5 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

Question 2, 3 (Q2, Q3) Exercise 1.5 Chapter 1 Class 9 Maths | Number Systems | NCERT, CBSE

English Version – Number System

The introductory video to understand the Number System has been created in English as well. You may watch this version in case you struggle to understand Hinglish.

Class 9 Chapter 2 | Polynomials

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Rational and Irrational numbers

Sunil Syal — Sun, 14 Feb 2021 05:47:34 +0000

Concept: Rational and irrational numbers constitute real numbers. Also, the set of rational and irrational numbers are mutually exclusive that means no number can be both rational and irrational. Symbols Q and Q′ (read it as Q-dash or Q-prime) are used to set of rational and irrational numbers respectively.

Rational Number

A number that can be written in the form of p/q where both p and q are integers and q ≠ 0.

A number that either has a finite decimal part like 2, 4.5 or has an infinite but recurring (repeating) decimal part like 4.6666…, 2.3456456…

Irrational Number

A number that cannot be written in the form of p/q where both p and q are integers and q ≠ 0.

A number that has an infinite and non-recurring (non-repeating) decimal part like

1.01001000100001…., √2, √3, 𝛑

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Number System

Sunil Syal — Wed, 27 Jan 2021 12:29:06 +0000

Concept: In this tutorial, you will learn about the very important topic – Number system. It is one of the basic concepts of Mathematics that every math student should learn very well. This is foundation of rest of the mathematics and should be very very clear to you. The tutorial not only covers and explains what different types of numbers are there but also explains what is the need of these numbers in real life.

The post Number System appeared first on Mathemafia.

Proof | Integers are infinitely many

Sunil Syal — Tue, 22 Sep 2020 13:42:31 +0000

Proof - Integers are Infinitely Many

Theorem: Prove that there are infinitely many integers.

Proof: Let us assume that there are finitely many Integers.

\( \begin{aligned} &\Rightarrow \text{∃ a greatest integer, say } x \end{aligned}\)

Let us get a new number say y by adding 1 to x.

\( \begin{aligned} y&=x+1\end{aligned}\)

\( \begin{aligned} &Now \ \ \mathbf{y} \in\mathbb{Z} \\ &\text{because } \mathbf{x+1} \text{ is also an integer}\\\\&But \ \ y > x \end{aligned}\)

So we got another integer y > x.

This is a contradiction to our assumption that x is the greatest integer.

This means our assumption is wrong that there are finitely many integers.

Hence we can conclude that there are infinitely many integers.

Watch on YouTube

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Mean method : Infinitely many rational numbers between any two rational numbers

Sunil Syal — Tue, 22 Sep 2020 13:36:47 +0000

Concept: In this tutorial, you will learn that there are infinitely many rational numbers between any two rational numbers. There are multiple ways to learn it and I have taught by calculating the mean (average) of two numbers.

Number System

Polynomials

Important Concepts – Miscellaneous

Derivation of Heron’s formula

Surface area and Volumes

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Proof – Rational numbers are infinitely many

Sunil Syal — Tue, 18 Aug 2020 14:17:26 +0000

Rational Number - Definition

Before we prove that there are infinitely many rational numbers, let us recall the definition of Rational Numbers.

A number that is of the form p/q where p and q are integers and q≠0 is called a rational number.

\( \begin{aligned} \frac{p}{q}\ \ \ \ where \ \ p,q\in\mathbb{Z}, \ \ q\ne0 \end{aligned}\)

Proof - Rational Numbers are Infinitely Many

Theorem: Prove that there are infinitely many rational numbers.

Proof: Let us assume that there are finitely many Rational Numbers.

\( \begin{aligned} &\Rightarrow \text{∃ a greatest rational number, say } x\\\\ &\Rightarrow x = \frac{p}{q} \ \ where \ \ p,q\in\mathbb{Z}, \ \ q\ne0 \end{aligned}\)

Let us get a new number say y by adding 1 to x.

\( \begin{aligned} y&=x+1\\\\ &=\frac{p}{q}+1\\\\ &=\frac{p+q}{q} \end{aligned}\)

\( \begin{aligned} &Now \ \ p+q \in\mathbb{Z}\\\\ &\Rightarrow y = \frac{p+q}{q} \ \ \text{is also a rational number}\\\\ &Now \ \ y > x \end{aligned}\)

This is a contradiction that x is the greatest rational number.

This means our assumption is wrong that there are finitely many rational numbers.

Hence we can conclude that there are infinitely many rational numbers.

Watch on YouTube

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Find a rational number between any two rational numbers

Sunil Syal — Tue, 18 Aug 2020 14:07:24 +0000

Concept: In this tutorial, you will learn to find a rational number between any two rational numbers by calculating the mean of the two numbers. It is quite simple method. There are more ways to find it, however, this is the easiest method. The tutorial is in Hindi.

Number System

Polynomials

Important Concepts – Miscellaneous

Derivation of Heron’s formula

Surface area and Volumes

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Commutative law explained for basic arithmetic operations

Sunil Syal — Sun, 16 Aug 2020 07:04:54 +0000

Concept: In this tutorial, you will learn about the commutative property (commutative law) and its applicability on different arithmetic operations. You will learn that addition and multiplication hold the commutative property where as subtraction and division does not.