REAL NUMBERS
•Download as PPTX, PDF•
5 likes•4,328 views
This document defines and categorizes different types of numbers and explains their representation on a number line. It discusses natural numbers, negative numbers, rational numbers, irrational numbers, and real numbers. It also describes properties of the number line including that numbers increase in value as you move right and decrease as you move left, and how to determine the distance between points on the number line using absolute value.
Report
Share
Report
Share
Recommended
1.1 Real Numbers and Number Operations
Use a number line to graph and order real numbers.
Identify properties of and use operations with real numbers.
1.1 real numbers & operations
1. The document discusses real numbers and their properties, including subsets such as rational and irrational numbers.
2. Key topics covered include using a number line to graph and order real numbers, properties of number operations like closure and commutativity, and defining operations like addition, subtraction, multiplication and division.
3. Unit analysis is also introduced to check that units make sense when performing number operations for real-life applications.
Real numbers
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
Real numbers system
The document discusses the real number system. It defines rational and irrational numbers, and provides examples of each. Rational numbers can be written as fractions, while irrational numbers can only be written as non-terminating and non-repeating decimals. The document also covers operations like addition, subtraction, multiplication, and division on integers, using rules like keeping or changing signs depending on whether the signs are the same or different.
1.3 Real Numbers and the Number Line
The document discusses classifying, graphing, and comparing real numbers, including finding and estimating square roots. It defines real numbers as numbers that can be located on the number line, including integers, rational numbers, and irrational numbers. The document also discusses the differences between finding the square root of a perfect square versus a non-perfect square.
Properties of Real Numbers
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
The Real Numbers
1) The document discusses the real number system, including identifying integers, rational numbers, and irrational numbers. Real numbers have important properties like closure under addition and multiplication.
2) Intervals of real numbers can be described using inequality notation like x ≥ 1 or -4 < x < 1, or interval notation like [1, +∞) or (-4, 1).
3) Absolute value of a real number a, written |a|, represents the distance of the number from the origin on the number line and is always non-negative.
Operations on Real Numbers
Real numbers include both positive and negative numbers. Operations can be performed on real numbers by following rules:
When adding like signs, add the absolute values and use the original sign. With different signs, find the difference of absolute values and use the greater sign.
For multiplication and division, a positive result occurs with same signs and negative result with different signs.
When raising a negative number to a power, the result is negative for odd exponents and positive for even exponents.
Recommended
1.1 Real Numbers and Number Operations
Use a number line to graph and order real numbers.
Identify properties of and use operations with real numbers.
1.1 real numbers & operations
1. The document discusses real numbers and their properties, including subsets such as rational and irrational numbers.
2. Key topics covered include using a number line to graph and order real numbers, properties of number operations like closure and commutativity, and defining operations like addition, subtraction, multiplication and division.
3. Unit analysis is also introduced to check that units make sense when performing number operations for real-life applications.
Real numbers
This document defines and explains key concepts related to real numbers and algebraic expressions. It introduces sets and subsets of real numbers like integers, rational numbers, and irrational numbers. It describes properties of real numbers including addition, multiplication, order, and absolute value. It also covers representing real numbers on a number line, algebraic expressions, and properties of negatives.
Real numbers system
The document discusses the real number system. It defines rational and irrational numbers, and provides examples of each. Rational numbers can be written as fractions, while irrational numbers can only be written as non-terminating and non-repeating decimals. The document also covers operations like addition, subtraction, multiplication, and division on integers, using rules like keeping or changing signs depending on whether the signs are the same or different.
1.3 Real Numbers and the Number Line
The document discusses classifying, graphing, and comparing real numbers, including finding and estimating square roots. It defines real numbers as numbers that can be located on the number line, including integers, rational numbers, and irrational numbers. The document also discusses the differences between finding the square root of a perfect square versus a non-perfect square.
Properties of Real Numbers
The document discusses properties of real numbers. It defines real numbers and distinguishes between rational and irrational numbers. Rational numbers can be expressed as ratios of integers, while irrational numbers have non-terminating, non-repeating decimals. It also outlines relationships between subsets of real numbers and properties that real number operations satisfy, such as commutativity, associativity, identities, inverses, and distribution.
The Real Numbers
1) The document discusses the real number system, including identifying integers, rational numbers, and irrational numbers. Real numbers have important properties like closure under addition and multiplication.
2) Intervals of real numbers can be described using inequality notation like x ≥ 1 or -4 < x < 1, or interval notation like [1, +∞) or (-4, 1).
3) Absolute value of a real number a, written |a|, represents the distance of the number from the origin on the number line and is always non-negative.
Operations on Real Numbers
Real numbers include both positive and negative numbers. Operations can be performed on real numbers by following rules:
When adding like signs, add the absolute values and use the original sign. With different signs, find the difference of absolute values and use the greater sign.
For multiplication and division, a positive result occurs with same signs and negative result with different signs.
When raising a negative number to a power, the result is negative for odd exponents and positive for even exponents.
Real Numbers & Number Lines (Geometry 2_1)
This document introduces several key concepts about real numbers and number lines:
1) Real numbers include both rational numbers (like integers and decimals) and irrational numbers.
2) A number line can be used to represent different sets of numbers, including whole numbers, integers, and rational numbers.
3) The coordinate of a point on a number line represents the real number associated with that point. The point where the number line crosses 0 is called the origin.
Math for 800 03 real numbers
Real Numbers for GMAT, GRE , SAT.
- Number Properties
- Real Numbers
- Number Line
- Basic Operations
Lesson 1.2 the set of real numbers
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
Rational numbers in the number line
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.
Real numbers
This document defines and provides examples of different types of real numbers including rational and irrational numbers. It discusses how rational numbers can be represented as fractions or decimals, and how to convert between fraction and decimal representations. Irrational numbers are defined as having non-terminating, non-repeating decimal representations. The key types of real numbers - natural numbers, integers, rational numbers, and irrational numbers - are related in a Venn diagram with their union being the set of all real numbers.
Introduction to rational no
This document discusses rational numbers. It defines rational numbers as numbers that can be written as fractions p/q where p and q are integers and q is not equal to 0. Some key properties of rational numbers are discussed, including that they are closed under addition, subtraction, and multiplication. Rational numbers exhibit commutativity and associativity with addition and multiplication, as well as distributivity of multiplication over addition and subtraction. The document also shows the locations of different number types including rational numbers on the number line.
Presentation on the real number system
The document discusses the real number system and different types of numbers. It defines natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers. It also discusses radicals, including the radicand, index, rational vs. irrational radicals, simplifying radicals using the multiplication property of radicals, and writing radicals in simplest form and mixed radicals as entire radicals.
Lecture 01 reals number system
The document discusses sets and operations involving sets of real numbers. It defines key sets such as the real numbers, rational numbers, integers, natural numbers, whole numbers, and irrational numbers. It also covers properties of real numbers like closure, commutativity, associativity, distributivity, identity, and inverse properties as they relate to addition and multiplication. Examples are provided to illustrate set notation and properties. The document contains exercises asking to identify which properties justify certain statements involving real number operations.
Subsets of real numbers
This document discusses different subsets of real numbers. It begins by explaining how primitive man counted using objects like stones and evolved to create number systems over hundreds of years. It then provides activities to identify subsets of numbers for different situations and defines key terms for subsets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Examples are given for each subset. Later, exercises are provided to identify which subset different numbers belong to.
Algebra 1 Slide Show
Algebra 1 covers different types of numbers including real numbers, which consist of rational and irrational numbers and can be thought of as existing on an infinite number line. It also discusses whole numbers as the counting numbers and 0, natural numbers as those first used to count, integers as numbers that can be positive, negative, or zero, rational numbers as fractions or quotients of integers, and irrational numbers as non-repeating decimals that cannot be represented as fractions.
The real Number system
The document discusses the real number system and different types of real numbers. It defines rational numbers as numbers that can be written as a fraction a/b, and irrational numbers as numbers that cannot be written as a fraction, such as the square root of 2. It provides examples of evaluating square roots and comparing real numbers using inequality symbols. It also covers ordering numbers from least to greatest and expressing decimals as rational numbers or repeating decimals.
TechMathII - 1.1 - The Set of Real Numbers
The document defines and provides examples of different types of numerical sets:
- Natural numbers are counting numbers like 1, 2, 3, etc.
- Whole numbers include natural numbers and 0.
- Integers include all whole numbers and their negatives.
- Rational numbers are numbers that can be written as fractions like a/b where a and b are integers.
- Irrational numbers cannot be written as fractions and include numbers like the square root of numbers and pi.
- Real numbers include all numbers, both rational and irrational.
1.1/1.2 Properties of Real Numbers
This document summarizes key concepts about expressions, equations, and inequalities in mathematics:
It defines variables, expressions, algebraic expressions, and different sets of real numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of real numbers like the additive inverse and multiplicative inverse. Examples are provided to illustrate graphing numbers and classifying them, as well as identifying properties from equations.
Real number system full
The document defines and explains the real number system by starting with natural numbers and expanding the number system to include rational numbers, irrational numbers, and finally real numbers. It provides examples and definitions of different types of numbers such as integers, fractions, periodic decimals. Properties of operations like addition, multiplication and equality on real numbers are also stated.
NS1: Rational and Irrational numbers
This document discusses rational and irrational numbers. Rational numbers can be written as fractions or repeating decimals, and include integers and perfect squares. Irrational numbers cannot be written as fractions and their decimals do not repeat, such as the square root of 2 or pi. Some key irrational numbers are discussed, which when calculated on a calculator either provide a non-terminating decimal or cause an error message. Rational numbers can be identified by determining if a number can be expressed as a ratio or fraction.
The real number system
John scored 17 points (4x4 + 0x1 + -1x3 = 17)
Mary scored 20 points (4x5 = 20)
Adam scored 18 points (4x4 + -1x2 = 18)
Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30)
Kim scored 31 points (4x7 + 4x1 = 31)
Jenny scored 32 points (4x8 = 32)
Zack scored 27 points (4x6 + 4x1 = 27)
Amy scored 25 points (4x5 + 4x1 = 25)
The students sorted from highest to lowest scores are:
1
Rational numbers
This document introduces real numbers and their properties. It discusses that real numbers can be divided into two kinds: rational numbers, which can be written as a ratio of integers, and irrational numbers, which cannot. It provides examples of rational numbers like fractions and decimals, as well as irrational numbers like square roots and pi. The document also defines integers, explains operations like exponents and identities, and illustrates the real number system.
Realnumbersystemnotes
The document discusses the real number system and its subsets. It defines natural numbers, whole numbers, integers, rational numbers, irrational numbers, terminating decimals, and repeating decimals. Rational numbers can be expressed as fractions, while irrational numbers are non-terminating and non-repeating decimals. The real number system is represented by a Venn diagram showing the relationships between its subsets. Examples are provided to demonstrate how to classify numbers as rational or irrational.
I can statements 7th grade cc math - ns
This document outlines key concepts and skills related to rational numbers including: representing addition and subtraction on a number line; identifying opposite numbers and describing situations where opposites add to zero; computing absolute value and understanding addition as the sum of a number and its distance from another; rewriting subtraction using additive inverses; applying properties of operations to add and subtract rational numbers; multiplying and dividing rational numbers while interpreting real-world situations; and converting rational numbers to decimals. The overall skills involve representing, comparing, adding, subtracting, multiplying, and dividing rational numbers, and applying these concepts to solve real-world problems.
Rational irrational and_real_number_practice
The document discusses real numbers and their classification. It defines real numbers as any number that can be found on the number line, including rational and irrational numbers. Rational numbers are those that can be written as fractions, with decimal forms that terminate or repeat. Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimal forms. Examples of rational numbers given include integers and fractions, while examples of irrational numbers include π and square roots of non-perfect squares. The document provides examples of classifying numbers as rational or irrational and ordering them on the number line.
Real numbers
Real numbers comprise all numbers that can be used in everyday life, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Real numbers represent unique points along the infinite number line. They include natural counting numbers and their positives, whole numbers with zero added, integers with their positives and negatives, rational numbers that can be written as fractions, and irrational numbers with non-terminating, non-repeating decimals.
Real Numbers
The document defines several subsets of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides examples for each set and discusses their properties. Rational numbers can be expressed as terminating or repeating decimals while irrational numbers are expressed as non-terminating, non-repeating decimals. The document also covers topics like the Euclid division algorithm, fundamental theorem of arithmetic, finding the highest common factor and least common multiple of numbers.
More Related Content
What's hot
Real Numbers & Number Lines (Geometry 2_1)
This document introduces several key concepts about real numbers and number lines:
1) Real numbers include both rational numbers (like integers and decimals) and irrational numbers.
2) A number line can be used to represent different sets of numbers, including whole numbers, integers, and rational numbers.
3) The coordinate of a point on a number line represents the real number associated with that point. The point where the number line crosses 0 is called the origin.
Math for 800 03 real numbers
Real Numbers for GMAT, GRE , SAT.
- Number Properties
- Real Numbers
- Number Line
- Basic Operations
Lesson 1.2 the set of real numbers
1. The document discusses subsets of real numbers including natural numbers, whole numbers, integers, and rational numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are formed by adding 0 to the natural numbers. Integers are formed by adding the negatives of natural numbers to whole numbers.
3. Rational numbers can be expressed as fractions a/b where a and b are integers and b is not equal to 0. Their decimal representations either terminate or repeat.
Rational numbers in the number line
1) Rational numbers are numbers that can be written as a quotient of two integers, such as a/b where b does not equal 0. They include integers as well as fractions and terminating or repeating decimals.
2) The document provides examples of rational numbers and asks students to determine if examples are rational numbers and to plot them on a number line.
3) Students are given practice locating rational numbers on a number line, such as -5/3, and asked to plot multiple rational numbers on a single number line.
Real numbers
This document defines and provides examples of different types of real numbers including rational and irrational numbers. It discusses how rational numbers can be represented as fractions or decimals, and how to convert between fraction and decimal representations. Irrational numbers are defined as having non-terminating, non-repeating decimal representations. The key types of real numbers - natural numbers, integers, rational numbers, and irrational numbers - are related in a Venn diagram with their union being the set of all real numbers.
Introduction to rational no
This document discusses rational numbers. It defines rational numbers as numbers that can be written as fractions p/q where p and q are integers and q is not equal to 0. Some key properties of rational numbers are discussed, including that they are closed under addition, subtraction, and multiplication. Rational numbers exhibit commutativity and associativity with addition and multiplication, as well as distributivity of multiplication over addition and subtraction. The document also shows the locations of different number types including rational numbers on the number line.
Presentation on the real number system
The document discusses the real number system and different types of numbers. It defines natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, imaginary numbers, and complex numbers. It also discusses radicals, including the radicand, index, rational vs. irrational radicals, simplifying radicals using the multiplication property of radicals, and writing radicals in simplest form and mixed radicals as entire radicals.
Lecture 01 reals number system
The document discusses sets and operations involving sets of real numbers. It defines key sets such as the real numbers, rational numbers, integers, natural numbers, whole numbers, and irrational numbers. It also covers properties of real numbers like closure, commutativity, associativity, distributivity, identity, and inverse properties as they relate to addition and multiplication. Examples are provided to illustrate set notation and properties. The document contains exercises asking to identify which properties justify certain statements involving real number operations.
Subsets of real numbers
This document discusses different subsets of real numbers. It begins by explaining how primitive man counted using objects like stones and evolved to create number systems over hundreds of years. It then provides activities to identify subsets of numbers for different situations and defines key terms for subsets like natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Examples are given for each subset. Later, exercises are provided to identify which subset different numbers belong to.
Algebra 1 Slide Show
Algebra 1 covers different types of numbers including real numbers, which consist of rational and irrational numbers and can be thought of as existing on an infinite number line. It also discusses whole numbers as the counting numbers and 0, natural numbers as those first used to count, integers as numbers that can be positive, negative, or zero, rational numbers as fractions or quotients of integers, and irrational numbers as non-repeating decimals that cannot be represented as fractions.
The real Number system
The document discusses the real number system and different types of real numbers. It defines rational numbers as numbers that can be written as a fraction a/b, and irrational numbers as numbers that cannot be written as a fraction, such as the square root of 2. It provides examples of evaluating square roots and comparing real numbers using inequality symbols. It also covers ordering numbers from least to greatest and expressing decimals as rational numbers or repeating decimals.
TechMathII - 1.1 - The Set of Real Numbers
The document defines and provides examples of different types of numerical sets:
- Natural numbers are counting numbers like 1, 2, 3, etc.
- Whole numbers include natural numbers and 0.
- Integers include all whole numbers and their negatives.
- Rational numbers are numbers that can be written as fractions like a/b where a and b are integers.
- Irrational numbers cannot be written as fractions and include numbers like the square root of numbers and pi.
- Real numbers include all numbers, both rational and irrational.
1.1/1.2 Properties of Real Numbers
This document summarizes key concepts about expressions, equations, and inequalities in mathematics:
It defines variables, expressions, algebraic expressions, and different sets of real numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of real numbers like the additive inverse and multiplicative inverse. Examples are provided to illustrate graphing numbers and classifying them, as well as identifying properties from equations.
Real number system full
The document defines and explains the real number system by starting with natural numbers and expanding the number system to include rational numbers, irrational numbers, and finally real numbers. It provides examples and definitions of different types of numbers such as integers, fractions, periodic decimals. Properties of operations like addition, multiplication and equality on real numbers are also stated.
NS1: Rational and Irrational numbers
This document discusses rational and irrational numbers. Rational numbers can be written as fractions or repeating decimals, and include integers and perfect squares. Irrational numbers cannot be written as fractions and their decimals do not repeat, such as the square root of 2 or pi. Some key irrational numbers are discussed, which when calculated on a calculator either provide a non-terminating decimal or cause an error message. Rational numbers can be identified by determining if a number can be expressed as a ratio or fraction.
The real number system
John scored 17 points (4x4 + 0x1 + -1x3 = 17)
Mary scored 20 points (4x5 = 20)
Adam scored 18 points (4x4 + -1x2 = 18)
Lisa scored 30 points (4x7 + 0x1 + -1x2 = 30)
Kim scored 31 points (4x7 + 4x1 = 31)
Jenny scored 32 points (4x8 = 32)
Zack scored 27 points (4x6 + 4x1 = 27)
Amy scored 25 points (4x5 + 4x1 = 25)
The students sorted from highest to lowest scores are:
1
Rational numbers
This document introduces real numbers and their properties. It discusses that real numbers can be divided into two kinds: rational numbers, which can be written as a ratio of integers, and irrational numbers, which cannot. It provides examples of rational numbers like fractions and decimals, as well as irrational numbers like square roots and pi. The document also defines integers, explains operations like exponents and identities, and illustrates the real number system.
Realnumbersystemnotes
The document discusses the real number system and its subsets. It defines natural numbers, whole numbers, integers, rational numbers, irrational numbers, terminating decimals, and repeating decimals. Rational numbers can be expressed as fractions, while irrational numbers are non-terminating and non-repeating decimals. The real number system is represented by a Venn diagram showing the relationships between its subsets. Examples are provided to demonstrate how to classify numbers as rational or irrational.
I can statements 7th grade cc math - ns
This document outlines key concepts and skills related to rational numbers including: representing addition and subtraction on a number line; identifying opposite numbers and describing situations where opposites add to zero; computing absolute value and understanding addition as the sum of a number and its distance from another; rewriting subtraction using additive inverses; applying properties of operations to add and subtract rational numbers; multiplying and dividing rational numbers while interpreting real-world situations; and converting rational numbers to decimals. The overall skills involve representing, comparing, adding, subtracting, multiplying, and dividing rational numbers, and applying these concepts to solve real-world problems.
Rational irrational and_real_number_practice
The document discusses real numbers and their classification. It defines real numbers as any number that can be found on the number line, including rational and irrational numbers. Rational numbers are those that can be written as fractions, with decimal forms that terminate or repeat. Irrational numbers cannot be written as fractions and have non-terminating, non-repeating decimal forms. Examples of rational numbers given include integers and fractions, while examples of irrational numbers include π and square roots of non-perfect squares. The document provides examples of classifying numbers as rational or irrational and ordering them on the number line.
What's hot (20)
Viewers also liked
Real numbers
Real numbers comprise all numbers that can be used in everyday life, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Real numbers represent unique points along the infinite number line. They include natural counting numbers and their positives, whole numbers with zero added, integers with their positives and negatives, rational numbers that can be written as fractions, and irrational numbers with non-terminating, non-repeating decimals.
Real Numbers
The document defines several subsets of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It provides examples for each set and discusses their properties. Rational numbers can be expressed as terminating or repeating decimals while irrational numbers are expressed as non-terminating, non-repeating decimals. The document also covers topics like the Euclid division algorithm, fundamental theorem of arithmetic, finding the highest common factor and least common multiple of numbers.
Number System
The document provides an overview of number systems used by different civilizations and an introduction to basic number concepts:
- It discusses ancient number systems including the Egyptian base-12 and Babylonian base-60 systems, as well as modern systems like binary and decimal.
- Basic number types are defined such as integers, rational numbers, irrational numbers, and real numbers. Fractions and decimal expansions are also introduced.
- Famous mathematicians who contributed to the study and development of number systems throughout history are acknowledged.
Real Numbers
This document is a lecture on real numbers presented by Ms. Cherry Rose R. Estabillo. It introduces the different subsets of real numbers from natural numbers to irrational numbers. Diagrams are shown to illustrate the relationships between these number sets. Examples are provided to demonstrate classifying numbers within these sets. Properties of real numbers like closure, commutativity, associativity and distributivity are discussed. The order of operations and examples applying it are also covered.
Slide03 Number System and Operations Part 1
The document discusses various number systems including decimal, binary, and signed binary numbers. It provides the following key points:
1) Decimal numbers use ten digits from 0-9 while binary only uses two digits, 0 and 1. Binary numbers represent values through place values determined by powers of two.
2) Conversions can be done between decimal and binary numbers through either summing the place value weights or repeated division/multiplication by two.
3) Binary arithmetic follows simple rules to add, subtract, multiply and divide numbers in binary representation.
4) Signed binary numbers use a sign bit to indicate positive or negative values, with the most common 2's complement form representing negative numbers as the 2's
Final maths presentation on sets
The document defines basic concepts about sets including:
- A set is a collection of distinct objects called elements. Sets can be represented using curly brackets or the set builder method.
- Common set symbols are defined such as belongs to (∈), is a subset of (⊆), and is not a subset of (⊄).
- Types of sets like empty sets, singleton sets, finite sets, and infinite sets are described.
- Operations between sets such as union, intersection, difference, and complement are explained using Venn diagrams.
- Laws for sets like commutative, associative, distributive, double complement, and De Morgan's laws are listed.
- An example problem calculates
Set Operations Topic Including Union , Intersection, Disjoint etc De Morgans ...
Set Operations Topic Including Union , Intersection, Disjoint etc De Morgans Prove With Important Examples For The Students Of B.Sc and F.Sc
Gameplay and ludology puzzles
This document contains three puzzles - a word puzzle, math puzzle, and picture puzzle. The word puzzle involves filling in missing four-letter words in a paragraph. The math puzzle involves filling in missing math operators to make equations correct. The picture puzzle hides two images within lines that can be rotated to reveal a camel resting and a sad boy resting his head on his knees.
Class9 number system
Rational numbers are numbers that can be represented as fractions p/q where p and q are integers and q is not equal to 0, such as 2/5 or 4/7. Irrational numbers are numbers that cannot be represented as fractions, such as √2 or √3, and their decimal representations are non-terminating and non-repeating. Real numbers include both rational and irrational numbers and can all be represented as unique points on a number line, with rational numbers having either terminating or non-terminating repeating decimals and irrational numbers having non-terminating, non-repeating decimals.
Module in solving quadratic equation
1. The document introduces a module on solving quadratic equations for high school students.
2. It discusses different methods for solving quadratic equations, including factoring, completing the square, using the quadratic formula, and graphing.
3. It also covers complex numbers and how to solve equations containing radicals or that can be reduced to quadratic equations.
Math Project
The document discusses different types of real numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Natural numbers can be defined as positive integers or non-negative integers. Whole numbers are sometimes used to refer to non-negative integers, positive integers, or all integers. Rational numbers are numbers that can be expressed as fractions, while irrational numbers like √2 have decimal expansions that continue forever without repeating.
1. sets and basic notations
A set is a collection of distinct objects called elements or members. A set can be defined using a roster method that lists the elements within curly brackets, or a rule method that describes a characteristic property that determines the elements. The cardinality of a set refers to the number of elements it contains, and can be finite or infinite.
Maths &Fun
This e-Twinning project between a 6th grade class in Romania and their teacher focused on problem solving in math. It included activities like cross-number puzzles, magic squares involving fractions, and having students search for math problems to solve. The goal was for students to practice problem solving skills in a fun way through collaborative online activities.
Matrices & determinants
The document defines matrices and provides examples of different types of matrices. It discusses key concepts such as rows, columns, dimensions, entries, addition, subtraction, and multiplication of matrices. It also covers special matrices like identity matrices, inverse matrices, transpose of matrices, and using matrices to solve systems of linear equations. The document is a comprehensive overview of matrices that defines fundamental terms and concepts.
Mathematics Sets and Logic Week 1
This document provides an overview of key concepts in sets and logic covered in Chapter 1, including:
- Basic symbols and terminology used in sets and logic
- Definitions of sets, set operations like union and intersection, and relationships between sets
- Properties of sets such as subsets, power sets, cardinality, and complement
- Algebraic laws governing set operations like distributive, associative, commutative, identity, and De Morgan's laws
- Methods of representing and reasoning about sets using mathematical notation and Venn diagrams
Operations on sets
The document defines and provides examples of different set operations:
1) Universal sets are sets that contain all other sets as subsets. The universal set of countries would be all countries.
2) Complements of a set are elements that are in the universal set but not in the given set. The complement of letters in "crush" would be other letters.
3) Unions of sets contain all unique elements of the sets combined. The union of sets {1,2,3} and {2,4} is {1,2,3,4}.
4) Intersections of sets contain only elements common to both sets. The intersection of sets {1,2,3} and {
Programed instructional material: Basics of Trignometry
This is an initial attempt by my students of B.Ed. in creating Programmed Instructional material using the template I had provided them. Your observations and suggestions are welcome!
Viewers also liked (20)
Set Operations Topic Including Union , Intersection, Disjoint etc De Morgans ...
Set Operations Topic Including Union , Intersection, Disjoint etc De Morgans ...
Programed instructional material: Basics of Trignometry
Programed instructional material: Basics of Trignometry
Similar to REAL NUMBERS
23T1W3 Mathematics ppt on Number Sequence.ppt
This document provides a lesson plan on number sequences and patterns. The objective is for students to be able to differentiate between positive and negative whole numbers, recognize and extend number sequences, and create reasonable sequences and patterns. It includes examples of number sequences, instructions for sequencing activities, and key words related to integers, sequences, patterns, increasing and decreasing numbers, and rules.
Integers and Absolute Value
This document discusses integers and absolute value. It defines integers as positive and negative whole numbers and explains how to graph and order integers on a number line. It also defines absolute value as the distance from zero and how to evaluate the absolute value of integers, including that the absolute value of a number can never be negative. Examples are provided for graphing, ordering, and finding opposites and absolute values of integers.
Rational Numbers.pptx
In this ppt slides, it includes all information about rational numbers. It start from natural numbers and at operations on rational numbers.
MATHEMATICS WORKBOOK FOR THE UNIT "REAL NUMBERS"
This document contains 6 worksheets with math problems focused on real numbers and number lines for 9th grade students. The worksheets include problems like calculating the length of a diagonal of a square, finding the perimeter of a circle, marking points and positions on number lines, identifying number ranges that satisfy conditions, calculating distances between numbers on a number line, and solving absolute value equations. The goal is to help students practice key concepts involving real numbers.
Lecture 1 (numbers and laws of indices)
This document provides an outline and information about real numbers, rational numbers, irrational numbers, integers, natural numbers, prime numbers, and indices/powers.
It begins by defining real numbers as any value that can be placed on a number line. Real numbers include rational numbers like integers and fractions, as well as irrational numbers like square roots. Rational numbers are those that can be written as a ratio of integers, while irrational numbers cannot. Several examples and questions are then provided to distinguish between rational and irrational numbers. Integers, natural numbers, and prime numbers are also defined.
The document concludes by covering indices/powers, their rules and evaluations. The rules of indices covered are exponent laws, negative exponents, zero
Introduction Combined Number And Dp
This document provides information about a mathematics module taught at the foundation level. It includes details such as the module title, code, credit hours, teaching periods, level, learning objectives, assessment types and course content. The module aims to reinforce basic numeracy and algebraic manipulation through lectures, seminars and tutorials. Students will be assessed through classroom tests, examinations and coursework assignments. The course content will cover topics such as numbers, operations, place value, and classifications of real numbers.
How To Make Multiplication Chart Without Knowing Your Times Tables
The document provides step-by-step instructions for creating a multiplication table on graph paper in two minutes or less. It explains how to fill in the numbers for the nines, fives, and twos rows by writing numbers in order or counting by the appropriate increments.
Hp33s calculator user_guide
This user guide provides instructions for operating the HP 33s scientific calculator. It covers turning the calculator on and off, using the keyboard and display, entering numbers, performing arithmetic, controlling the display format, using fractions, entering and evaluating equations, programming the calculator, and more. The guide includes appendices that cover batteries, memory, ALG mode, solving, integrating, and error messages.
[Maths] Sequences 2003 Bis
The document discusses various types of numeric and non-numeric sequences, including natural numbers, even/odd numbers, powers of numbers, the Fibonacci sequence, prime numbers, days of the week, months of the year, and the Spanish alphabetic and numeric systems. Examples of each type of sequence are provided in multiple lines of repeating numbers.
Integers
Integers are the collection of whole numbers and their negatives. There are two types of integers: positive integers like 1, 2, 3, etc. and negative integers like -1, -2, -3, etc. Integers are ordered on the number line, with positive integers to the right of zero and negative integers to the left. Addition and subtraction of integers follows sign rules - integers with the same sign are added/subtracted normally, and integers with different signs are subtracted but keep the sign of the larger integer. Integers are used in daily calculations like balances that can be positive or negative. Multiplication and division of integers also follows consistent sign rules.
Inequaility
This document contains exercises on linear inequalities from a math class. Exercise 1.1 defines terms related to inequalities. Exercises 1.2-1.3 require students to solve linear inequalities and check their work. Exercise 1.4 instructs students to graph solutions to inequalities on a number line. Exercise 1.5 poses multiple choice and short answer questions testing understanding of inequalities.
Number System2.pptx
This document provides information about different types of numbers. It begins by defining what a number system is and discusses how numbers are used to quantify various things. It then defines what a number is mathematically. Various types of real numbers like rational and irrational numbers are categorized. Specific types of numbers like odd, even, prime, composite etc. are defined along with examples. Methods to represent numbers like 2 and 3 are shown visually on a number line. Converting between rational numbers and decimal expansions is discussed along with examples. Laws of exponents and irrational numbers are stated.
Math for 800 04 integers, fractions and percents
This document provides information about integers, even and odd numbers, consecutive numbers, prime numbers, factors and divisors, fractions, and operations with fractions such as addition and subtraction. It defines key terms and provides examples. Sections include integers and their values, properties of even and odd numbers, consecutive integers, prime numbers and tests for divisibility. Later sections cover factors and divisors, prime factorization, greatest common factor (GCF), least common multiple (LCM), remainders, and equivalent fractions.
Class_Powerpoint_Sequences_Arithmetic_and_Geometric_with_Series_Finite_and_In...
1. The document discusses arithmetic and geometric sequences.
2. Arithmetic sequences are defined by adding a common difference to get the next term, while geometric sequences multiply by a common ratio.
3. Examples are provided of finding terms in arithmetic and geometric sequences using formulas.
Update manual
Our company is mainly engaged in developing, producing cutting machine from 1998.AOKE is the first computer carton sample company in china in 2003, export AOKE cutting machine plotter to overseas markets in 2005.AOKE cutting machine plotter sales is over Switzerland's first (ZUND) cutting machine plotter in 2007. AOKE is the first Global sales in 2008.
AOKE plotter cutting machine application sectors
A) Packaging printing industry
B) Frame-lined cardboard processing
C) Laser knife mold and hand knife mold industry
D) Shoe pattern cutting machine
E)costume cutting machine plotter
F) handbag cutting machine plotter
G)electronic material industry
H) Advertising LGP light box glasswork acrylic pmma V cutter groove engraving machine
Looking forward to hearing from you soon.
Website: www.gdaoke.com/en/index.asp
E-mail: aokecut@163.com
MSN aokecut@163.com
SKPYE :aokecut
ICQ: 638681509
Office phone:+0086-769-22901766
Fax NO. +0086-769-22901769
Mobile phone :+0086-15916997282
contact person Mrs betty
Update manual
Our company is mainly engaged in developing, producing cutting machine from 1998.AOKE is the first computer carton sample company in china in 2003, export AOKE cutting machine plotter to overseas markets in 2005.AOKE cutting machine plotter sales is over Switzerland's first (ZUND) cutting machine plotter in 2007. AOKE is the first Global sales in 2008.
AOKE plotter cutting machine application sectors
A) Packaging printing industry
B) Frame-lined cardboard processing
C) Laser knife mold and hand knife mold industry
D) Shoe pattern cutting machine
E)costume cutting machine plotter
F) handbag cutting machine plotter
G)electronic material industry
H) Advertising LGP light box glasswork acrylic pmma V cutter groove engraving machine
Looking forward to hearing from you soon.
Website: www.gdaoke.com/en/index.asp
E-mail: aokecut@163.com
MSN aokecut@163.com
SKPYE :aokecut
ICQ: 638681509
Office phone:+0086-769-22901766
Fax NO. +0086-769-22901769
Mobile phone :+0086-15916997282
contact person Mrs betty
EOY MATHS
This document appears to be an exam paper for mathematics. It contains 20 multiple part questions testing a variety of math skills, including algebra, geometry, statistics, and trigonometry. The exam is divided into clearly labeled sections and provides space for students to show their work. It instructs students on exam rules and provides references to formulas.
4 ma0 4hr_que_20150112
This document appears to be an exam paper for mathematics. It contains 20 multiple part questions testing a variety of math skills, including algebra, geometry, statistics, and trigonometry. The exam is divided into clearly labeled sections and provides space for students to show their work. Instructions are provided at the beginning regarding time, materials, and how to fill out identifying information.
Learn matlab primer
This document provides information about MATLAB, including how to contact The MathWorks for sales, support, or to access the user community. It describes the copyright and trademark policies for MATLAB. The revision history shows that this primer has been updated over time to correspond with new MATLAB releases since 1996.
Similar to REAL NUMBERS (20)
How To Make Multiplication Chart Without Knowing Your Times Tables
How To Make Multiplication Chart Without Knowing Your Times Tables
Class_Powerpoint_Sequences_Arithmetic_and_Geometric_with_Series_Finite_and_In...
Class_Powerpoint_Sequences_Arithmetic_and_Geometric_with_Series_Finite_and_In...
More from Sariga Vinod
AREA OF QUADRILATERALS
This document discusses triangles ABC and ADC, which share the same base AB. It shows that the sum of the areas of the two triangles is equal to the area of the whole figure, which is the sum of the two triangles. Specifically, the area of triangle ABC plus the area of triangle ADC is equal to the area of the whole quadrilateral figure P1 + P2.
FEATURES OF TRIANGLES
This document discusses the formulas for finding the areas of triangles and rectangles. It notes that the area of a rectangle is twice the area of a triangle formed by two vertices on the rectangle's side and the third vertex on the opposite side. The document also discusses how triangles between parallel lines that have the same base are equal in area.
TYPES OF QUADRILATERALS
This document defines and provides properties of seven shapes: rectangle, square, parallelogram, rhombus, trapezium, isosceles trapezium, and quadrilateral. It states that rectangles and squares have opposite sides that are equal and parallel and angles of 90 degrees, while parallelograms and rhombuses have opposite sides that are equal and parallel and opposite angles that are equal. Trapeziums have one pair of opposite sides that are parallel, and isosceles trapeziums have one pair of opposite sides that are parallel and non-parallel sides that are equal. Quadrilaterals have no defining properties listed.
AREA OF TRIANGLE
The document discusses the area formula for right-angled triangles and how it can be applied to other triangles. It states that the area of any triangle can be calculated as _1 = bh^2, where b is the base and h is the height. It then shows that both acute and obtuse triangles sharing the same base and height between parallel lines have the same area as a right-angled triangle with those dimensions, following the same area formula.
TYPES OF TRIANGLES
This document discusses the properties of triangles and three-sided polygons. It notes that a triangle has three vertices and three interior angles that sum to 180 degrees, while the three exterior angles sum to 360 degrees. It then defines a right triangle as having one 90 degree angle and identifies the base, height, and hypotenuse. The document also states that all angles in a triangle are less than 90 degrees, except for one angle in an obtuse triangle which is greater than 90 degrees.
AREA OF TRIANGLES
This document discusses the formulas for finding the areas of triangles and rectangles. It notes that the area of a rectangle is twice the area of a triangle formed by two vertices on the rectangle's side and the third vertex on the opposite side. The document also discusses how triangles between parallel lines that have the same base are equal in area.
LESSON PLAN ONE
This lesson plan is about teaching negative numbers to students. It begins with an introduction to the concept of negative numbers and their properties. Examples of expressions with negative numbers like x*(-z)+y*(-z)=(x+y)*(-z) are shown. The lesson will involve students doing activities with activity cards involving calculations with negative numbers. They will then discuss the differences between positive and negative numbers and situations where negatives are used. Formative assessment questions are included to check student understanding.
INNOVATIVE LESSON TEMPLATE
The document outlines an innovative lesson template for teaching the topic of "Classification of Lives into Three Stages" in Class 8 Pohimkv{Xw (Philosophy). The lesson aims to help students understand the classification of lives into three stages through discussion, analysis, and examples. It includes an analysis of key terms and facts about the five stages (sam\od, t{]m ́oÃw, ^wssP, πmt‚, A\ntaenb), learning outcomes, teaching-learning activities like presentations and group discussions, and a follow-up activity where students describe two characters from each stage. The lesson allows students to comprehend the different characteristics of lives in each stage and the
INNOVATIVE LESSON PLAN
This lesson plan outlines a 45-minute social science class on different forms of money used as substitutes for cash. The teacher will introduce demand drafts, cheques, and ATM/debit cards by showing examples and explaining what each is and how it functions as money. Students will participate in activities where the teacher discusses the key features and differences between each type of substitute money using slides. Finally, the class will review the different forms of money and their merits to reinforce what was learned.
Jiji
This lesson plan introduces students to different forms of money as substitutes for cash, including demand drafts, cheques, and ATM/debit cards. The teacher will engage students through activities using visual aids like slides and flashcards to explain each payment method. Students will learn that demand drafts allow banks to transfer money between branches, cheques let account holders make payments or withdrawals, and ATMs are automated machines for 24/7 cash access. The lesson aims to help students identify, compare, and understand the merits and demerits of non-cash payment options.
Jiji
This lesson plan is about different forms of money used as substitutes for cash. The teacher will discuss demand drafts, cheques, and ATM/debit cards. Through a presentation and activities, students will learn that demand drafts allow individuals to access money through banks, cheques can be used by account holders to withdraw or transfer money, and ATMs are automated machines that allow customers to access their bank accounts without staff. The lesson aims to identify various money substitutes and compare their features.
More from Sariga Vinod (11)
Recently uploaded
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh
HYPERTENSION - SLIDE SHARE PRESENTATION.
IT WILL BE HELPFULL FOR THE NUSING STUDENTS
IT FOCUSED ON MEDICAL MANAGEMENT AND NURSING MANAGEMENT.
HIGHLIGHTS ON HEALTH EDUCATION.
Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47
Event Link:- https://meetups.mulesoft.com/events/details/mulesoft-mysore-presents-mule-event-processing-models/
Agenda
● What is event processing in MuleSoft?
● Types of event processing models in Mule 4
● Distinction between the reactive, parallel, blocking & non-blocking processing
For Upcoming Meetups Join Mysore Meetup Group - https://meetups.mulesoft.com/mysore/YouTube:- youtube.com/@mulesoftmysore
Mysore WhatsApp group:- https://chat.whatsapp.com/EhqtHtCC75vCAX7gaO842N
Speaker:-
Shivani Yasaswi - https://www.linkedin.com/in/shivaniyasaswi/
Organizers:-
Shubham Chaurasia - https://www.linkedin.com/in/shubhamchaurasia1/
Giridhar Meka - https://www.linkedin.com/in/giridharmeka
Priya Shaw - https://www.linkedin.com/in/priya-shaw
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...Nguyen Thanh Tu Collection
https://app.box.com/s/tacvl9ekroe9hqupdnjruiypvm9rdaneGender and Mental Health - Counselling and Family Therapy Applications and In...
A proprietary approach developed by bringing together the best of learning theories from Psychology, design principles from the world of visualization, and pedagogical methods from over a decade of training experience, that enables you to: Learn better, faster!
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
Certified as an ISO/IEC 27001: Information Security Management Systems (ISMS) Lead Implementer, Data Protection Officer, and Cyber Risks Analyst, Denis brings a heightened focus on data security, privacy, and cyber resilience to every endeavor.
His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
What sets Denis apart is his comprehensive understanding of Business and Systems Analysis technologies, honed through involvement in all phases of the Software Development Lifecycle (SDLC). From meticulous requirements gathering to precise analysis, innovative design, rigorous development, thorough testing, and successful implementation, he has consistently delivered exceptional results.
Throughout his career, he has taken on multifaceted roles, from leading technical project management teams to owning solutions that drive operational excellence. His conscientious and proactive approach is unwavering, whether he is working independently or collaboratively within a team. His ability to connect with colleagues on a personal level underscores his commitment to fostering a harmonious and productive workplace environment.
Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
-------------------------------------------------------------------------------
Find out more about ISO training and certification services
Training: ISO/IEC 27001 Information Security Management System - EN | PECB
ISO/IEC 42001 Artificial Intelligence Management System - EN | PECB
General Data Protection Regulation (GDPR) - Training Courses - EN | PECB
Webinars: https://pecb.com/webinars
Article: https://pecb.com/article
-------------------------------------------------------------------------------
For more information about PECB:
Website: https://pecb.com/
LinkedIn: https://www.linkedin.com/company/pecb/
Facebook: https://www.facebook.com/PECBInternational/
Slideshare: http://www.slideshare.net/PECBCERTIFICATION
A Visual Guide to 1 Samuel | A Tale of Two Hearts
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
BBR 2024 Summer Sessions Interview Training
Qualitative research interview training by Professor Katrina Pritchard and Dr Helen Williams
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Recently uploaded (20)
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Traditional Musical Instruments of Arunachal Pradesh and Uttar Pradesh - RAYH...
Film vocab for eal 3 students: Australia the movie
Film vocab for eal 3 students: Australia the movie
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
Mule event processing models | MuleSoft Mysore Meetup #47
Mule event processing models | MuleSoft Mysore Meetup #47
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 9 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2024-2025 - ...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
Gender and Mental Health - Counselling and Family Therapy Applications and In...
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
REASIGNACION 2024 UGEL CHUPACA 2024 UGEL CHUPACA.pdf
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.ppt
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
ISO/IEC 27001, ISO/IEC 42001, and GDPR: Best Practices for Implementation and...
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) Curriculum
REAL NUMBERS
- 3. Numbers which are used to count things are known as NATURAL NUMBERS.
- 5. NEGETIVE NUMBERS -1,-2,-3,-4……………………………… This type of numbers , which having a negative sign are known as NEGATIVE NUMBERS
- 6. RATIONAL NUMBERS NATURAL NUMBERS NEGATIVE NUMBERS ZERO, FRACTIONS AND THEIR NEGATIVES collectively known as RATIONAL NUMBERS
- 7. IRRATIONAL NUMBERS The numbers which are not rational are IRRATIONALS
- 8. IRRATIONAL NUMBERS Eg. √2, √3, √5, Π…………….
- 9. REAL NUMBERS The numbers RATIONALS and IRRATIONALS Together known as REAL NUMBERS
- 10. NUMBER LINE
- 11. LINE WHICH CONTAINS ALL REAL NUMBERS AS POINTS.
- 12. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9
- 13. RATIONAL NUMBERS ON NUMBER LINE
- 14. . . . . . . . . . . . . . . . . . . . -4 -3 -2 -1 0 1/2 1 2 3 4 -3/2
- 15. IRRATIONAL NUMBERS ON NUMBER LINE
- 16. -9-8-7 -6-5-4 -3 -2-1 √2 1 2 3 4 5 6 7 8 9 . . . . . . . . . . . . . . . . . . .
- 17. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 1 2 3 4 5 6 7 8 9 .Π 0
- 18. SMALL AND LARGE LEFT AND RIGHT
- 19. WHEN WE GOES THROUGH RIGHT SIDE OF A NUMBER LINE THE VALUE OF THE POINTS ARE INCREASES.
- 20. WHEN WE GOES THROUGH LEFT SIDE OF A NUMBER LINE THE VALUE OF THE POINTS ARE DECREASES.
- 21. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 2<x<4
- 22. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 -3<x<2
- 23. DISTANCES
- 24. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 2 UNITS
- 25. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 2 UNITS
- 26. . . . . . . . . . . . . . . . . . . . -9-8-7 -6-5-4 -3 -2-1 0 1 2 3 4 5 6 7 8 9 6 UNITS
- 28. DISTANCE FROM ZERO TO ANY POINT x /x/
- 29. /x/ = X , if x>0 -X , if x<0 0 , if x=]0
- 30. DISTANCE BETWEEN ANY TWO POINTS X and Y /X-Y/