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# NCERT Solutions for class 9 Maths Chapter 1 Exercise 1.3 Number Systems - PDF Download

Class 9 NCERT solutions for class 9 maths chapter 1 ex 1.3 presents a different approach to the concept of rational and irrational numbers. Students will be introduced to the concept of the decimal expansion of real numbers and how it can be used to distinguish between rational and irrational figures.

Students will also use their decimal expansions to represent real numbers on a number line. However, it is important to note that the decimal expansion of an irrational number is non-terminating and non-recurring. In addition, a non-terminating and  non-recurring decimal expansion number is an irrational number. NCERT solutions class 9 maths chapter 1 ex 1.3 is composed of 9 questions. Out of the 9 questions, 7 are short answer types and 4 are long answer types.

NCERT solutions for Class 9 provide a comprehensive and sequential explanation of each answer to the questions in the ex 1.3. eSaral offers a downloadable free PDF of NCERT solutions for class 9 maths chapter 1 ex 1.3. These solutions can be used to gain a better comprehension of the questions of ex 1.3.

## Topics Covered in Exercise 1.3 class 9 Mathematics Questions

NCERT solutions class 9 maths chapter 1 ex 1.3 explains the decimal expansion of real numbers. Here, you will get the detailed explanation of this topic.

 1 Real Numbers and Their Decimal Expansions
1. Real Numbers and Their Decimal Expansions - The real numbers can be written in the decimal form. The long division method can be used to write the real numbers in the decimal expansion whose values are numerically equal to the real number. The decimal expansion of the real numbers is nothing more than the simplification of the real numbers.

Real Numbers

Real numbers are the combination of rational numbers and irrational numbers. All real numbers can be represented on a number line. imaginary numbers are non-real numbers which cannot be represented on a number line.

Decimal Expansions

Before delving into a numerical representation of the decimal extension of rational numbers, it is important to comprehend the concept of rational numbers. A rational number is a numerical expression that can be expressed in the form p/q, in which p and q are integers and q ≠ 0 respectively. Examples of rational numbers include 2/3, 1/4, 4/5, etc. The symbol for a rational number is Q. As all integers can be expressed in p / q form, all Integers can be considered rational numbers.

Generally, there are three types of decimals expansion:

1. Terminating

2. Non-terminating Repeating

3. Non-terminating Non Repeating

4. Terminating Decimals - The term "terminating decimals" is used to describe decimal numbers that have only a finite number of digits. That means the number comes to end after a decimal point after a certain number of repetitions. Examples = 0.875, 0.5, 2.556 etc.

5. Non-terminating Repeating - Non-terminating decimal numbers are those decimal numbers which have an infinite number of digits. In this case, the number does not terminate. Examples = 1.33333….., 52.36363636…, 2.343537684904… etc.

Repeating Decimals - In mathematics, repeating decimals refer to numerical expressions in which a particular number is repeated uniformly after a single decimal point. Examples = 0.5555…, 13.262626…, 1.8769876…, etc.

Non-terminating and repeating decimals are rational numbers. These can be represented in the form p/q, where q ≠ 0.

1. Non-terminating Non Repeating - In Non repeating decimals, the number is not repeated in a uniform manner. Example = 4.345627238…, 1.61803398…, 2.718281828459… etc.

Non-terminating and non-repeating decimals are irrational numbers, and cannot be represented as p/q.

## Tips for Solving Exercise 1.3 class 9 chapter 1 Number Systems

The NCERT solutions class 9 maths chapter 1 ex 1.3 is concerned with the real number system and its expansion into decimal form. Therefore, it is essential for students to be familiar with the fundamentals of decimal numbers and their intricate calculations in order to successfully complete the exercise. Here are some important tips to solve ex 1.3 questions.

1. Real numbers may appear complex at first, but with regular practice, students will be able to master the fundamentals.

2. NCERT solutions class 9 maths chapter 1 ex 1.3 will provide students with an in-depth comprehension of the fundamental principles of the number system, which will be beneficial to comprehension of higher maths.

## Importance of Solving Ex 1.3 class 9 Maths chapter 1 Number Systems

Solving questions of ex 1.3 class 9 maths chapter 1 will provide you a lot of benefits.

1. NCERT class 9 maths syllabus 1.3 provides us with an in-depth understanding of the numerical system, which is helpful for us to comprehend higher mathematics.

2. By solving the NCERT solution for class 9 maths chapter 1 ex 1.3, you can also learn how to represent real numbers on the number line using the decimal expansions.

3. Ex 1.3 in class 9 maths covers the fundamental facts about decimals and how they are represented on the number line, which helps us to solve the exercise questions easily.