Real Numbers
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MATH 101 REAL NUMBERS Lecture by: Ms. Cherry Rose R. Estabillo ALGEB-X: REAL NUMBER SYSTEM MATH101 C. ESTABILLO
description
MATH 101 REAL NUMBERS Lecture by: Ms. Cherry Estabillo
Transcript of Real Numbers
MATH 101
REAL NUMBERS
Lecture by: Ms. Cherry Rose R. Estabillo
ALGEB-X: REAL NUMBER SYSTEM
MATH101 C. ESTABILLO
Real Numbers
Rational Numbers
Irrational Numbers
Non- Integers
Integers
Negative Integers
Whole Numbers
Zero
Natural Numbers
MATH101 C. ESTABILLO
Real Numbers
Rational Numbers
Irrational Numbers
Non- Integers
Integers
Negative Integers
Whole Numbers
Zero
Natural Numbers
MATH101 C. ESTABILLO
Schematic Diagram
NaturalNumbers
(N)
N = {1, 2, 3, 4, …}
MATH101 C. ESTABILLO
Schematic Diagram
Whole Numbers (W)
NaturalNumbers
(N)
W = {0, 1, 2, 3, 4, …}
MATH101 C. ESTABILLO
Schematic Diagram
Integers (Z)
Whole Numbers (W)
NaturalNumbers
(N)
Z = {… -2, -1, 0, 1, 2, …}
MATH101 C. ESTABILLO
Schematic Diagram
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
NaturalNumbers
(N)
Q = { … -3, … 0, … 3, … }
-3.75
5/7
-2
4.21
A rational number can be expressed as a quotient of two integers, a/b where b is not equal to 0. The set of rational numbers includes terminating and repeating decimals.
MATH101 C. ESTABILLO
Schematic Diagram
2
Irrational Numbers(Q’)
Q’ = { … -3, … 0, … 3, … }
-1.1234567890023…
3 3
An irrational number is a non-repeating, non-terminating decimal.
MATH101 C. ESTABILLO
Schematic Diagram
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
NaturalNumbers
(N)
Irrational Numbers
Real Numbers
MATH101 C. ESTABILLO
Example
Given:
Name the set of non-integer, rational numbers.Name the set of irrational numbers.Name the set of integers.Name the set of whole numbers.Name the set of natural numbers.
81,2...,253253.9,25,
2
1,0...,71253.2,,3,
2,
11
8,14.3,30 i
MATH101 C. ESTABILLO
Properties of Real Numbers
• Closure Property
• Commutative Property
• Associative Property
• Distributive Property of Multiplication over Addition
• Identity Property
• Inverse Property
• Zero Property
MATH101 C. ESTABILLO
Name the axiom that justifies the ff. statement
MATH101 C. ESTABILLO
)530(2020)530(
xxxxx 22424
135)135( xx
405040500
37
Application
• Is the action of undressing and taking a bath commutative?
• Is the action of tying your left shoe and tying your right shoe commutative?
MATH101 C. ESTABILLO
ORDER OF OPERATIONS
P E M D A S
MATH101 C. ESTABILLO
EXAMPLES1.) 56 ÷ 23 x 7 –1 + 3 x 8
2.)
MATH101 C. ESTABILLO
3148)3(
243240
