Explain real numbers in brief?

Question

Answer

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line. ... The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number).

Answer

The set of rational number and irritational number are real numbers..

Answer

Real no are the group of rational and irrational numbers  like root3, 5! and 1/4 etc

Answer

Real numbers are the collection of rational and irrational numbers. It is represented by R on the number line and each real number is represented by a unique point on the number line. An irrational number is a real number but a real cannot be always an irrational number as it consists of both rational and irrational numbers.Example of irrational number :√5,0.7486785,π etc.example of rational number:2,4,6etc which can be represented in the form of p/q where p and q are integers and q not equal to zero.

Answer

Real Numbers

Real numbers are a classification of numbers that include all rational and irrational numbers. They are the numbers that can be represented on a number line, and they form the basis of our numerical system. Real numbers can be positive, negative, or zero, and they can be whole numbers, fractions, or decimals.

Classification of Real Numbers

Real numbers can be classified into three main categories: rational numbers, irrational numbers, and integers.

Rational Numbers:
Rational numbers can be expressed as a fraction or a ratio of two integers. They can be positive, negative, or zero. Examples of rational numbers include 3/4, -2/5, and 0.

Irrational Numbers:
Irrational numbers cannot be expressed as a fraction or a ratio of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include √2, π (pi), and e.

Integers:
Integers are whole numbers (positive, negative, or zero) and their opposites. They do not include fractions or decimals. Examples of integers include -3, 0, and 5.

Real Number Line:
The real number line is a horizontal line that represents all real numbers. It extends infinitely in both directions and is divided into positive and negative sections. The zero point is the origin of the number line.

Properties of Real Numbers:
Real numbers have several important properties:

1. Closure Property: The sum, difference, or product of any two real numbers is also a real number.
2. Commutative Property: The order of addition and multiplication does not affect the result.
3. Associative Property: The grouping of numbers in addition and multiplication does not affect the result.
4. Distributive Property: Multiplication distributes over addition.
5. Identity Property: The sum of any real number and zero is the number itself. The product of any real number and one is the number itself.
6. Inverse Property: Every real number has an additive inverse (opposite) and a multiplicative inverse (reciprocal).

Conclusion:
Real numbers encompass all rational and irrational numbers. They are represented on a number line and have various properties that make them essential in mathematics. Understanding real numbers is fundamental in many mathematical concepts and applications.

Top Courses for Class 9View all

Science Class 9

Social Studies (SST) Class 9

Mathematics (Maths) Class 9

English Class 9

English Grammar Advanced

Top Courses for Class 9

Top Courses for Class 9

Suggested Free Tests

Related Content

Class 9 Study Material

Class 9 Subjects

Competitive Examinations for Class 9

NCERT Books

NCERT Solutions

Reference Books for Class 9

Other Popular Exams

Company