NCERT Solutions for Class 9 Political Science Chapter 2

August 8, 202239 Insightful Publications

**NCERT Solutions for Class 9 Maths Chapter 1: **Expert professors at Embibe have developed NCERT solutions for Class 9 Maths chapter 1: Number Systems. These NCERT Class 9 Maths chapter 1 solutions help the students in tackling challenges skillfully and effectively in their preparation for board exams. These solutions also make problems simple enough for the students to understand.

The goal of the NCERT Class 9 chapter 1 solutions is to provide students with step-by-step explanations for each concept in the chapter. These Class 9 chapter 1 Maths NCERT solutions are very reliable and should be used by students as their primary study material. Continue reading this article to learn more about the NCERT solutions for Class 9 Maths in detail.

Before jumping into further details about Class 9 Maths chapter 1, here is an overview of the topics and sub-topics in NCERT solutions for Class 9 Maths chapter 1:

Section | Topic Name |
---|---|

1.1 | Introduction |

1.2 | Irrational Number |

1.3 | Real Numbers and Their Decimal Expansions |

1.4 | Representing Real Numbers on the Number Line |

1.5 | Operations on Real Numbers |

1.6 | Laws of Exponents for Real Numbers |

1.7 | Summary |

The Number System represents different kinds of numbers like binary numbers, decimal numbers, natural numbers, rational numbers, prime numbers, whole numbers, and various other types. In this chapter, multiple notions are used to represent these numbers. Students will learn how to describe the numbers on the number line. They will also perform some operations with rational and irrational numbers and learn about the laws of exponents.

In this chapter, students will also learn that a number system is called a rational number if it can be written in the form of p/q, the decimal expansion of a rational and irrational number. All the real numbers and irrational numbers are collectively called real numbers. Students can refer to the PDF link to download the NCERT solutions to study offline:

Here are a few questions and their solutions which students can use in their preparation for exams:

**Q.1. Is zero a rational number? Can you write it in the form of pq, where p and q are integers and q≠0?**

**Solution: **A number ‘r’ is said to be a rational number, if it can be represented in the form pq, where p and q are integers and q≠0.

The number 0 can be written as: 01 or 02 or 03… or 0n, where n can be any integer, except 0.

Since 0 can be represented in the pq form, where q≠0, Hence, zero is a rational number.

**Q.2. Find six rational numbers between 3 and 4.**

**Solution:** We know that, an infinite number of rational numbers are present between 3 and 4.

To find six of these numbers, let us first represent 3 and 4 as rational numbers with denominator 6+1=7.

Multiplying and dividing the numbers by 7, we get, 3=3×77=217 and 4=4×77=287 The required rational numbers will be the numbers which are in between 217 and 287. Therefore, six rational numbers between 3 and 4 are 227, 237, 247, 257, 267, 277.

**Q.3. Find five rational numbers between 35 and 45.**

**Solution:** There are a infinite number of rational numbers between 35 and 45.

We can find them, by multiplying and dividing the numerator and denominator by the same number.

We can choose any number to multiply and divide but ideally, we choose the number that is more than the required number of rational numbers So, let us choose 7. Now, 35=3×75×7=2135

and 45=4×75×7=2835. Therefore, the required numbers are 2235,2335,2435,2535,2635.

**Note: **There are a infinite number of rational numbers in between two given rational numbers, so answer is not unique. It depends upon the numbers you have taken.

**Download NCERT Solutions Class 9 Maths Chapter 1 PDF**

Following are the important points in NCERT solutions for Class 9 for Maths chapter 1:

- A number r is called a rational number, if it can be written in the form p/q , where p and q are integers and q ≠ 0.
- A number s is called an irrational number, if it cannot be written in the form p/q , where p and q are integers and
- q ≠ 0.
- The decimal expansion of a rational number is either terminating or non-terminating recurring. Moreover, a number whose decimal expansion is terminating or non-terminating recurring is rational.
- The decimal expansion of an irrational number is non-terminating and non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is irrational.
- All the rational and irrational numbers make up the collection of real numbers.
- There is a unique real number corresponding to every point on the number line. Also, corresponding to each real number, there is a unique point on the number line.
- If r is rational and s is irrational, then r + s and r – s are irrational numbers, and rs and r/s are irrational numbers, r ≠ 0.
- For positive real numbers a and b, the following identities hold:
- ⎷ab = ⎷a ⎷b
- ⎷a/b = ⎷a ⎷b
- ( ⎷a+⎷b) (⎷a-⎷b) = a-b
- (a+⎷b ) (a-⎷b ) = a
^{2}– b - (⎷a+⎷b)
^{2}= a+ 2⎷ab + b

- To rationalise the denominator of 1/⎷a+b, we multiply this by , ⎷a-b/⎷a-b, where a and b are integers.
- Let a > 0 be a real number and p and q be rational numbers. Then,
- a
^{p}. a^{q}= a^{p + q} - (a
^{p})^{ q}= a^{pq} - a
^{p }/ a^{q}= a^{p-q} - a
^{p}b^{p}= (ab)^{p}

- a

Embibe has listed some important questions based on the basic concepts covered in this chapter. Practice them and join Embibe for more sample questions and mock tests to improve the performance in the Class 9 Maths exam.

Q.1: Show how √5 can be represented on the number line.

Q.2: Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is rational.

Q.3: Write three numbers whose decimal expansions are non-terminating and non-recurring.

Q.4: Find three different irrational numbers between the rational numbers 5/7 and 9/11.

Q.5: Visualise 3.765 on the number line using successive magnification.

Q.6: Visualise 4. √26, the number line, up to 4 decimal places.

Some of the benefits of NCERT solutions for Class 9 Maths chapter 1 are mentioned below:

- The NCERT solutions for Class 9 Maths chapter 1 helps students practice, solve and revise all the important concepts covered in this chapter.
- After going through the step-wise solutions provided by our subject experts, students can score maximum marks in their Maths exams.
- The NCERT solution provides answers to all the exercises or in-text questions for reference and learning.
- It contains all the important questions from the examination point of view.
- Students can check the NCERT solutions and work on their weaknesses.

Mathematics is a very scoring subject. Students need to understand all concepts clearly and apply formulae correctly. Rigorous practice for all chapters is a must to solve questions step-wise for the Class 9 final exam.

Below, Embibe has provided some of the preparation tips for Class 9 Maths exam:

- Focus on learning concepts of each topic.
- For each topic, make separate notes. Write all formulae covered under it with an illustration for each. This will help students know when to apply the formula.
- Practice as many questions as you can on each topic, and you will be able to solve questions of different difficulty levels
- Take mock tests to learn time management to get the time to review the solutions.
- Students can mug up some formulas but practice them enough to know when to apply them.
- Focus on the NCERT books and solve all questions given in them.
- Make a list of all the silly mistakes and solve enough questions to prevent them in the final paper.

**Ans:** The concepts are explained in simple language in the NCERT solutions for Class 9 chapter 1 Maths by Embibe. The NCERT solutions are prepared by a team of experts at Embibe to help students enhance their exam preparation

** Ans: **In Class 9 Maths chapter 1, “Number System”, students will learn that a number system is called a rational number if it can be written as p/q, the decimal expansion of a rational and irrational number, what is a real number.

**Ans:** The exercises covered in NCERT chapter 1 of Class 9 Maths are as follows:

1) Exercise 1.1: 4 Questions (4 short answers)

2) Exercise 1.2: 4 Questions (4 short answers)

3) Exercise 1.3: 9 Questions (8 short answers, 1 long answer)

4) Exercise 1.4: 2 Questions (2 long answers)

5) Exercise 1.5: 5 Questions (4 short answers, 1 long answer)

6) Exercise 1.6: 3 Questions (3 short answers).

**Ans:** The NCERT solutions by Embibe will help students understand the chapter better. The NCERT solutions for chapter 1 of Class 9 Maths have been explained in a step-by-step and detailed manner so that any student can understand them.

**Ans:** Students can download the chapter for free from Embibe, and in return, they get tricks, tips, and notes that they can revise at the last minute before the exam. This will help the students to score well.