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RD Sharma Class 10 Solutions Chapter 1 - Real Numbers (Ex 1.3) Exercise 1.3

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RD Sharma Class 10 Solutions Chapter 1 - Real Numbers (Ex 1.3) Exercise 1.3 - Free PDF

Free PDF download of RD Sharma Class 10 Solutions Chapter 1 - Real Numbers Exercise 1.3 solved by Expert Mathematics Teachers on Vedantu. All Chapter 1 - Real Numbers Ex 1.3 Questions with Solutions for RD Sharma to help you to revise complete Syllabus and Score More marks. Register for online coaching for IIT JEE (Mains & Advanced) and other Engineering entrance exams.

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RD Sharma Class 10 Solutions Chapter 1 - Real Numbers (Ex 1.3)

Introduction to the Chapter

All numbers in the real world are called real numbers. Class 10 Chapter Real Numbers is a high-scoring topic that required a little practice. Class 10 Students should solve RD Sharma of this Chapter to gain more confidence and score full marks from this Chapter.


Different Number Sets in Real Numbers

Real Numbers consist of a large set of numbers. These include-

  • Natural Numbers

  • Whole Numbers

  • Integers

  • Rational Numbers

  • Irrational Numbers


Properties of Real Numbers

  • Closure Property of Real Numbers:

The closure property of Real Numbers states that the sum and product of 2 real numbers is always a real number. The closure property is mathematically stated as follows: If a, b ∈ R, a + b ∈ R, and ab ∈ R

  • Associative Property of Real Numbers:

 The sum or product of any 3 real numbers remains the same when the grouping of numbers is changed. The associative property is mathematically stated as follows: If a,b,c ∈ R, a + (b + c) = (a + b) + c and a × (b × c) = (a × b) × c

  • Commutative Property of Real Numbers: 

The sum and the product of 2 real numbers always remain the same after interchanging the order of the numbers. The commutative property is mathematically stated as follows: If a, b ∈ R, a + b = b + a and a × b = b × a

  • Distributive Property of Real Numbers: 

Real numbers satisfy the distributive property. The distributive property of multiplication over addition can also be said as- a × (b + c) = (a × b) + (a × c) and the distributive property of multiplication over subtraction is seen as- a × (b - c) = (a × b) - (a × c)

FAQs on RD Sharma Class 10 Solutions Chapter 1 - Real Numbers (Ex 1.3) Exercise 1.3

1. What are some properties of Irrational Numbers?

The numbers which cannot be denoted in a fractional form (p/q) are called Irrational Numbers. Some properties of irrational numbers are- They consist of both, non-terminating and non-recurring decimals.


Irrational Numbers are real numbers 


When an irrational and a rational number are added, their sum is always an irrational number only.


When any of the irrational numbers are multiplied by any non-zero rational number, their product is always an irrational number. 


For any two given irrational numbers, their Least Common Multiple (LCM) may not exist.

The addition, multiplication, subtraction, and division of two irrational numbers may or may not be a rational number.

2. Is 0 both a whole number and a natural number?

0 is a whole number but not a Natural Number. In the number system,  Natural numbers are described to all the positive integers from 1 to infinity. Natural numbers are also known as counting numbers as they do not include zero or negative numbers. While on the other hand, Whole Numbers are natural numbers, but with a 0. The only difference between Whole Numbers and Natural Numbers is that Whole Numbers contain 0 and Natural Numbers do not.

3. What is the difference between Integers and Real Numbers?

The major difference between real numbers and integers is that integers are real numbers but real numbers are not integers. Real numbers include number sets such as rational numbers, whole numbers, natural numbers, and irrational numbers whole Integers include positive numbers, zero, and negative numbers. Real numbers are represented by the letter 'R' while integers are represented by the letter 'Z'. On a number line, every point depicts a unique real number while only whole numbers and negative numbers denote integers on a number line. These are the major differences between integers and Real numbers.

4. How to study Class 10 real numbers for full marks?

To get full marks in any subject, the students have to do plenty of practice. Especially in maths where the question paper is full of numerical questions. Getting full marks in Class 10 Real Numbers will require the child to solve good questions that will help them clear their fundamentals. Class 10 students can start with solving NCERT and then move on to reference books such as RD Sharma. RD Sharma has many solved examples that will assist the child to understand the method of approaching questions. This is how a Class 10 student can bring full marks in real numbers Chapter.

5. How to represent all types of Real Numbers on a number line?

A number line helps us to display numbers by representing them by a unique point on the line. Every point on the number line depicts a unique real number. To represent real numbers a number line, follow the steps below:


Step 1: Draw one horizontal line with arrows on both ends. Then mark the number 0 in the middle and 0 is called the origin.

Step 2: Mark equal lengths on both sides of the origin and label them with a definite scale.

Step 3: The student should mark positive numbers lying on the right side of the origin and the negative numbers lying on the left side of the origin.

This is how a student can represent Real Numbers on a number line.