1. Real and Rational
Numbers
Name Aayush Jha
Sub code GE3B- 02
Subject Basic Mathamatics & statistics
Year 1st
year ( 2nd
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.
