real and rational number ppt it shows real number

ppr

1. Real and Rational Numbers Name Aayush Jha Sub code GE3B- 02 Subject Basic Mathamatics & statistics Year 1 st year ( 2 nd sem ) CALCUTTA INSTITUTE OF SCIENCE AND MANAGEMENT

2. Introduction This presentation will explore the concepts of real numbers and rational numbers, including their definitions, properties, and differences.

3. Real Numbers Real numbers include all rational and irrational numbers. Rational numbers can be written as fractions, while irrational numbers cannot be expressed as fractions. Real numbers are represented on the number line, covering both positive and negative values, including zero. They are used in everyday calculations and mathematical operations. Examples include numbers like 2, -3, 1/2, √2, and π.

4. Definition and Examples Real numbers include all the numbers that can be found on the number line. This includes whole numbers, fractions, and decimals. Examples of real numbers are -3, 0, 1/2, and 2.75.

5. Properties of Real Numbers Real numbers possess several properties: the closure property (sums and products of real numbers are real), the commutative property (order doesn't matter in addition or multiplication), and the associative property (grouping doesn't affect the results).

6. Types of Real Numbers Real numbers can be classified into various types: natural numbers (counting numbers), whole numbers (natural numbers plus zero), integers (whole numbers and their negative counterparts), rational numbers (numbers that can be expressed as a fraction), and irrational numbers (numbers that cannot be expressed as fractions, like π and √2).

7. Rational Numbers Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. They include integers, fractions, and terminating or repeating decimals. Every rational number can be represented on the number line. Examples include 3/4, -2, 0.5, and 7. Rational numbers are used in various calculations and real-life situations.

8. Definition and Examples Rational numbers are numbers that can be expressed as a fraction a/b, where a and b are integers, and b is not zero. Examples include 1/2, -4, and 0.75 (which can be expressed as 3/4).

9. Properties of Rational Numbers Rational numbers possess unique properties: they are closed under addition, subtraction, multiplication, and division (except division by zero). They can be represented in decimal form, which can either terminate or repeat periodically.

10. Comparison with Irrational Numbers Rational numbers differ from irrational numbers in that rational numbers can be precisely expressed as a fraction, while irrational numbers cannot. Examples of irrational numbers include π and √2, which are non-repeating and non-terminating decimals.

11. Conclusions In summary, understanding real and rational numbers is foundational in mathematics. They play crucial roles in various applications and enhance our ability to perform calculations and comprehend numerical relationships.

12. Thank you !