Classifying Numbers
•Download as PPTX, PDF•
2 likes•2,478 views
Rational numbers can be written as fractions or terminating decimals, while irrational numbers are non-repeating and non-terminating decimals that cannot be expressed as fractions. The document provides examples of rational numbers like 3/1, 3/2, 1/9, 4, and 7/1000. Examples of irrational numbers given include the square root of 2 and pi, which have non-repeating decimals. The document includes interactive exercises asking the user to identify numbers as rational or irrational.
Report
Share
Report
Share
Recommended
Rational and irrational numbers by Kashae Alexander
To multiply rational numbers, convert them to decimals and multiply the decimals.
Rational numbers are fractions with a numerator and denominator, while irrational numbers go on indefinitely as decimals and cannot be expressed as fractions.
When multiplying a rational number and an irrational number, the result will always be irrational, as it is not possible to express an irrational number as a fraction.
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.
9.2 rational and irrational numbers day 1
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as fractions or ratios, including integers, terminating decimals, and repeating decimals. Irrational numbers are defined as numbers that cannot be written as fractions or repeating/terminating decimals, such as the square root of a non-perfect square. Examples are provided to demonstrate how to determine if a number is rational or irrational based on its decimal representation.
Y10 m27012015numbarith1
This document provides information about real numbers, rational numbers, irrational numbers, basic arithmetic operations involving rational and irrational numbers, approximation by rounding decimals to a certain number of decimal places or significant figures, and percentage calculations. It includes definitions of rational numbers as numbers that can be written as fractions, irrational numbers as numbers that cannot be written as fractions, and examples of rounding decimals and solving percentage word problems involving finding a percentage of a number, finding the original number given its percentage, and calculating percentage increases and decreases.
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.
Rational numbers
This document discusses operations with rational numbers such as addition, subtraction, multiplication, and division. It explains that for addition and subtraction of rational numbers with common denominators, only the numerators are added or subtracted. For different denominators, the lowest common denominator must first be found before adding or subtracting the numerators. Multiplication of rational numbers is done by multiplying the numerators and denominators. Division can be performed by multiplying the first number by the reciprocal of the second number.
Rational and irrational numbers
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as p/q where p and q are integers and q is not equal to 0. Rational numbers include fractions, integers, and natural numbers. The document describes the different types of rational numbers such as positive, negative, and in standard form. It also discusses how to perform operations like addition, subtraction, multiplication, and division on rational numbers. Irrational numbers are defined as real numbers that cannot be expressed as a ratio of integers like the roots of prime numbers or pi.
Number system for class Nine(IX) by G R Ahmed TGT(Maths) at K V Khanapara
Here are the answers with explanations:
(i) True. Every natural number is a whole number. The set of natural numbers is a subset of the set of whole numbers.
(ii) True. Every integer is a whole number. The set of integers contains the set of whole numbers.
(iii) False. Not every rational number is a whole number. Rational numbers also include fractions and terminating/repeating decimals.
(iv) True. Every irrational number is a real number. The set of irrational numbers is a subset of the set of real numbers.
(v) False. Not every real number is irrational. The set of real numbers contains both rational and irrational numbers.
(vi
Recommended
Rational and irrational numbers by Kashae Alexander
To multiply rational numbers, convert them to decimals and multiply the decimals.
Rational numbers are fractions with a numerator and denominator, while irrational numbers go on indefinitely as decimals and cannot be expressed as fractions.
When multiplying a rational number and an irrational number, the result will always be irrational, as it is not possible to express an irrational number as a fraction.
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.
9.2 rational and irrational numbers day 1
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as fractions or ratios, including integers, terminating decimals, and repeating decimals. Irrational numbers are defined as numbers that cannot be written as fractions or repeating/terminating decimals, such as the square root of a non-perfect square. Examples are provided to demonstrate how to determine if a number is rational or irrational based on its decimal representation.
Y10 m27012015numbarith1
This document provides information about real numbers, rational numbers, irrational numbers, basic arithmetic operations involving rational and irrational numbers, approximation by rounding decimals to a certain number of decimal places or significant figures, and percentage calculations. It includes definitions of rational numbers as numbers that can be written as fractions, irrational numbers as numbers that cannot be written as fractions, and examples of rounding decimals and solving percentage word problems involving finding a percentage of a number, finding the original number given its percentage, and calculating percentage increases and decreases.
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.
Rational numbers
This document discusses operations with rational numbers such as addition, subtraction, multiplication, and division. It explains that for addition and subtraction of rational numbers with common denominators, only the numerators are added or subtracted. For different denominators, the lowest common denominator must first be found before adding or subtracting the numerators. Multiplication of rational numbers is done by multiplying the numerators and denominators. Division can be performed by multiplying the first number by the reciprocal of the second number.
Rational and irrational numbers
This document discusses rational and irrational numbers. It defines rational numbers as numbers that can be written as p/q where p and q are integers and q is not equal to 0. Rational numbers include fractions, integers, and natural numbers. The document describes the different types of rational numbers such as positive, negative, and in standard form. It also discusses how to perform operations like addition, subtraction, multiplication, and division on rational numbers. Irrational numbers are defined as real numbers that cannot be expressed as a ratio of integers like the roots of prime numbers or pi.
Number system for class Nine(IX) by G R Ahmed TGT(Maths) at K V Khanapara
Here are the answers with explanations:
(i) True. Every natural number is a whole number. The set of natural numbers is a subset of the set of whole numbers.
(ii) True. Every integer is a whole number. The set of integers contains the set of whole numbers.
(iii) False. Not every rational number is a whole number. Rational numbers also include fractions and terminating/repeating decimals.
(iv) True. Every irrational number is a real number. The set of irrational numbers is a subset of the set of real numbers.
(v) False. Not every real number is irrational. The set of real numbers contains both rational and irrational numbers.
(vi
Terminating non terminating class 10 groupA
it is maths presentation of class 10th on terminating or non-terminating. It contains attractive animations and good amount of information related to topic. The purpose of this presentation is to increase your knowledge
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.
Wednesdayweek7
The document defines key terms related to fractions, including numerator, denominator, proper fraction, improper fraction, equivalent fractions, simplest form, lowest terms, and reciprocal. It provides instructions for simplifying, multiplying, dividing, and converting fractions to decimals. Key steps outlined include multiplying the numerators and denominators to multiply fractions, and dividing the numerator by the denominator to write a fraction as a decimal. Repeating and terminating decimals are defined.
Real Numbers class 9
This document defines and provides examples of different types of real numbers:
- Real numbers include all natural numbers, whole numbers, integers, rational numbers, and irrational numbers. They comprise every number that can be found on the number line.
- Natural numbers are counting numbers starting from 1. Whole numbers are natural numbers with 0 added. Integers include natural numbers and their negatives. Rational numbers are numbers that can be written as fractions. Irrational numbers are numbers that cannot be written as fractions.
- Examples demonstrate addition and subtraction of integers using rules such as keeping the sign the same for addition/subtraction of like signs, and changing the sign for addition/subtraction of opposite signs. Multiplication and division
Numebr system
This document discusses different types of numbers. It begins with counting numbers which start from 1 and have no largest number. Natural numbers also start from 1 and are infinite. Whole numbers include 0 and are also infinite. Integers include both positive and negative numbers and have an equal and opposite number for every integer. Rational numbers are numbers that can be represented as fractions. Real numbers include both rational numbers like fractions as well as irrational numbers like pi which have non-terminating, non-repeating decimals. The real number set contains all other number sets.
Holiday homework
This document discusses rational numbers. It provides definitions of rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators. It describes the different types of rational numbers and how to write them in standard form. The document also discusses the basic mathematical operations of addition, subtraction, multiplication and division that can be performed on rational numbers. It provides examples of how to apply these operations. Finally, it discusses some real-world applications and uses of rational numbers.
natural numbers ppt for class 9 th
The document discusses different types of number systems including natural numbers, whole numbers, rational numbers, integers, and irrational numbers. It provides definitions and examples of each type of number system. Natural numbers are used for counting and include zero depending on the system. Whole numbers include all natural numbers and zero. Rational numbers include integers and fractions. Integers include both positive and negative whole numbers. Irrational numbers have decimal values that continue forever without repeating patterns, such as pi.
number system class 9
This document introduces different number systems, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It defines each type of number and provides examples. Rational numbers can be written as fractions using integers, while irrational numbers cannot be expressed as ratios of integers. Together, rational and irrational numbers make up the set of real numbers, which correspond one-to-one with points on the real number line. Famous mathematicians like Pythagoras, Cantor, and Dedekind contributed to the understanding and classification of these different number systems.
Introduction To Simplifying Fractions
1) The document discusses equivalent fractions and how fractions can represent the same quantity even if written differently.
2) It provides examples of how 1/2 is equivalent to 2/4 because both represent one of two equal parts of a whole.
3) The key to finding equivalent fractions is to divide both the numerator and denominator by a common factor to simplify the fraction into equivalent lower terms.
Introduction to Rational numbers
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
Real Numbers
Real numbers include rational and irrational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers, such as integers, repeating decimals, and terminating decimals. Irrational numbers are numbers that cannot be expressed as a ratio of integers and continue endlessly without a repeating pattern, such as the square root of two and pi. Real numbers comprise all numbers including rational numbers like integers and irrational numbers.
Real Numbers
This document defines and provides examples of different types of real numbers:
- Rational numbers can be written as ratios of integers and have terminating or repeating decimals. Irrational numbers cannot be written as ratios and have non-terminating, non-repeating decimals.
- Real numbers include rational and irrational numbers. Rational numbers further include integers, whole numbers, and natural numbers. Integers are whole numbers and their opposites, whole numbers are positive integers and zero, and natural numbers are counting numbers.
- Examples are provided to illustrate the different types of numbers and how to classify numbers like π, √4, and 3/4.
Number Systems
Real numbers include rational numbers like integers and fractions as well as irrational numbers like square roots and pi. Real numbers can be represented on a continuous number line and include both countable and uncountable infinite numbers. Real numbers have the properties of a field where they can be added, multiplied, and ordered on the number line in a way compatible with these operations. Rational numbers are numbers that can be represented as fractions of integers, and they include integers, whole numbers, and natural numbers. Irrational numbers cannot be represented as fractions.
Powerpoint real numbers
The real numbers consist of rational numbers like integers, fractions, and repeating decimals as well as irrational numbers like square roots and pi. Real numbers have the properties that between any two real numbers there are an infinite number of real numbers, and real numbers are closed under addition, subtraction, multiplication, and division except by zero. Rational numbers can be written as fractions of integers, while irrational numbers cannot be written as fractions.
Real numbers
Real numbers include all numbers that can be used in everyday life and represented on the number line. They comprise integers, rational numbers like fractions, irrational numbers with non-repeating decimals, natural numbers starting at 1, and whole numbers including 0. Integers include natural numbers and their negatives. Rational numbers can be written as fractions, while irrational numbers have non-repeating decimals. Order of operations and properties like commutativity, associativity, and distributivity govern mathematical operations on real numbers.
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.
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.
Real numbers system
Real numbers include decimals, fractions, integers, rational numbers like fractions and repeating decimals, and irrational numbers like pi. They can be positive or negative, and are organized on a number line that extends infinitely in both directions. Real numbers are grouped into categories including counting numbers, whole numbers, integers, rational numbers, and irrational numbers.
π
Pi (π) is an irrational number because it cannot be expressed as a simple fraction or ratio. While some fractions like 22/7 can approximate pi, they eventually diverge from pi's true non-terminating, non-repeating decimal value. Therefore, pi is not a rational number that can be written as a simple ratio, but rather an irrational number that continues infinitely without repetition or pattern.
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.
Irrational Numbers
Irrational numbers are any numbers that cannot be expressed as a quotient of two integers. Examples of irrational numbers include the square root of 2 and the square root of 30. To determine if a principal root is rational or irrational, check if the radicand is a perfect nth power - if it is, the root is rational, otherwise it is irrational. Estimating square roots involves finding the two closest perfect squares that are less than and greater than the number inside the radical.
1.2 Irrational Numbers ppt
This document discusses square roots and irrational numbers. It defines that the square of an integer is a perfect square, and taking the square root is the opposite of squaring a number. Examples are provided of finding the number that produces a square of 81, which is 9, but -9 also works. The document also defines rational and irrational numbers, noting that square roots of perfect squares are rational, while square roots of non-perfect squares are irrational.
More Related Content
What's hot
Terminating non terminating class 10 groupA
it is maths presentation of class 10th on terminating or non-terminating. It contains attractive animations and good amount of information related to topic. The purpose of this presentation is to increase your knowledge
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.
Wednesdayweek7
The document defines key terms related to fractions, including numerator, denominator, proper fraction, improper fraction, equivalent fractions, simplest form, lowest terms, and reciprocal. It provides instructions for simplifying, multiplying, dividing, and converting fractions to decimals. Key steps outlined include multiplying the numerators and denominators to multiply fractions, and dividing the numerator by the denominator to write a fraction as a decimal. Repeating and terminating decimals are defined.
Real Numbers class 9
This document defines and provides examples of different types of real numbers:
- Real numbers include all natural numbers, whole numbers, integers, rational numbers, and irrational numbers. They comprise every number that can be found on the number line.
- Natural numbers are counting numbers starting from 1. Whole numbers are natural numbers with 0 added. Integers include natural numbers and their negatives. Rational numbers are numbers that can be written as fractions. Irrational numbers are numbers that cannot be written as fractions.
- Examples demonstrate addition and subtraction of integers using rules such as keeping the sign the same for addition/subtraction of like signs, and changing the sign for addition/subtraction of opposite signs. Multiplication and division
Numebr system
This document discusses different types of numbers. It begins with counting numbers which start from 1 and have no largest number. Natural numbers also start from 1 and are infinite. Whole numbers include 0 and are also infinite. Integers include both positive and negative numbers and have an equal and opposite number for every integer. Rational numbers are numbers that can be represented as fractions. Real numbers include both rational numbers like fractions as well as irrational numbers like pi which have non-terminating, non-repeating decimals. The real number set contains all other number sets.
Holiday homework
This document discusses rational numbers. It provides definitions of rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators. It describes the different types of rational numbers and how to write them in standard form. The document also discusses the basic mathematical operations of addition, subtraction, multiplication and division that can be performed on rational numbers. It provides examples of how to apply these operations. Finally, it discusses some real-world applications and uses of rational numbers.
natural numbers ppt for class 9 th
The document discusses different types of number systems including natural numbers, whole numbers, rational numbers, integers, and irrational numbers. It provides definitions and examples of each type of number system. Natural numbers are used for counting and include zero depending on the system. Whole numbers include all natural numbers and zero. Rational numbers include integers and fractions. Integers include both positive and negative whole numbers. Irrational numbers have decimal values that continue forever without repeating patterns, such as pi.
number system class 9
This document introduces different number systems, including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It defines each type of number and provides examples. Rational numbers can be written as fractions using integers, while irrational numbers cannot be expressed as ratios of integers. Together, rational and irrational numbers make up the set of real numbers, which correspond one-to-one with points on the real number line. Famous mathematicians like Pythagoras, Cantor, and Dedekind contributed to the understanding and classification of these different number systems.
Introduction To Simplifying Fractions
1) The document discusses equivalent fractions and how fractions can represent the same quantity even if written differently.
2) It provides examples of how 1/2 is equivalent to 2/4 because both represent one of two equal parts of a whole.
3) The key to finding equivalent fractions is to divide both the numerator and denominator by a common factor to simplify the fraction into equivalent lower terms.
Introduction to Rational numbers
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
Real Numbers
Real numbers include rational and irrational numbers. Rational numbers are numbers that can be expressed as a ratio of two integers, such as integers, repeating decimals, and terminating decimals. Irrational numbers are numbers that cannot be expressed as a ratio of integers and continue endlessly without a repeating pattern, such as the square root of two and pi. Real numbers comprise all numbers including rational numbers like integers and irrational numbers.
Real Numbers
This document defines and provides examples of different types of real numbers:
- Rational numbers can be written as ratios of integers and have terminating or repeating decimals. Irrational numbers cannot be written as ratios and have non-terminating, non-repeating decimals.
- Real numbers include rational and irrational numbers. Rational numbers further include integers, whole numbers, and natural numbers. Integers are whole numbers and their opposites, whole numbers are positive integers and zero, and natural numbers are counting numbers.
- Examples are provided to illustrate the different types of numbers and how to classify numbers like π, √4, and 3/4.
Number Systems
Real numbers include rational numbers like integers and fractions as well as irrational numbers like square roots and pi. Real numbers can be represented on a continuous number line and include both countable and uncountable infinite numbers. Real numbers have the properties of a field where they can be added, multiplied, and ordered on the number line in a way compatible with these operations. Rational numbers are numbers that can be represented as fractions of integers, and they include integers, whole numbers, and natural numbers. Irrational numbers cannot be represented as fractions.
Powerpoint real numbers
The real numbers consist of rational numbers like integers, fractions, and repeating decimals as well as irrational numbers like square roots and pi. Real numbers have the properties that between any two real numbers there are an infinite number of real numbers, and real numbers are closed under addition, subtraction, multiplication, and division except by zero. Rational numbers can be written as fractions of integers, while irrational numbers cannot be written as fractions.
Real numbers
Real numbers include all numbers that can be used in everyday life and represented on the number line. They comprise integers, rational numbers like fractions, irrational numbers with non-repeating decimals, natural numbers starting at 1, and whole numbers including 0. Integers include natural numbers and their negatives. Rational numbers can be written as fractions, while irrational numbers have non-repeating decimals. Order of operations and properties like commutativity, associativity, and distributivity govern mathematical operations on real numbers.
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.
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.
Real numbers system
Real numbers include decimals, fractions, integers, rational numbers like fractions and repeating decimals, and irrational numbers like pi. They can be positive or negative, and are organized on a number line that extends infinitely in both directions. Real numbers are grouped into categories including counting numbers, whole numbers, integers, rational numbers, and irrational numbers.
π
Pi (π) is an irrational number because it cannot be expressed as a simple fraction or ratio. While some fractions like 22/7 can approximate pi, they eventually diverge from pi's true non-terminating, non-repeating decimal value. Therefore, pi is not a rational number that can be written as a simple ratio, but rather an irrational number that continues infinitely without repetition or pattern.
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.
What's hot (20)
Viewers also liked
Irrational Numbers
Irrational numbers are any numbers that cannot be expressed as a quotient of two integers. Examples of irrational numbers include the square root of 2 and the square root of 30. To determine if a principal root is rational or irrational, check if the radicand is a perfect nth power - if it is, the root is rational, otherwise it is irrational. Estimating square roots involves finding the two closest perfect squares that are less than and greater than the number inside the radical.
1.2 Irrational Numbers ppt
This document discusses square roots and irrational numbers. It defines that the square of an integer is a perfect square, and taking the square root is the opposite of squaring a number. Examples are provided of finding the number that produces a square of 81, which is 9, but -9 also works. The document also defines rational and irrational numbers, noting that square roots of perfect squares are rational, while square roots of non-perfect squares are irrational.
Power point presentation
This document defines irrational numbers as real numbers that cannot be expressed as a ratio of integers or as a decimal. It provides examples of common irrational numbers such as pi, the golden ratio, e, and the square root of 2. These numbers are irrational because their values continue infinitely without repeating patterns, and thus cannot be written as exact fractions. The document also notes how Pythagoras' theorem relates to rational and irrational numbers in right triangles.
Irrational numbers
This document discusses irrational numbers, which are numbers that cannot be expressed as a ratio of two integers, such as the square root of 2. It provides examples of irrational numbers that arise from calculations involving the sides of geometric shapes, such as the square root of 2 being the length of the diagonal of a unit square. The document also covers operations involving irrational numbers, stating that the product and quotient of irrational numbers are irrational numbers.
Irrational numbers
This document proves that the square root of any prime number is irrational. It first states the definition of an irrational number as a real number that cannot be expressed as a ratio of integers. It then proves by contradiction that if p is a prime number, square root of p is irrational. It assumes square root of p is rational, and derives a contradiction using the Fundamental Theorem of Arithmetic. It provides additional examples of proving irrational numbers using this method of proof by contradiction.
Scientific notation
This document provides information about a math lesson on scientific notation. It discusses writing, adding, and subtracting numbers in scientific notation. Examples are given to show how to express large numbers like the estimated number of stars in the universe in scientific notation. The lesson wrap up reminds students that scientific notation allows determining the order of magnitude of a number and that tomorrow's lesson will cover computing with numbers in this notation. Students are assigned independent practice problems to complete.
2 (2.1) intro number sense
The document discusses different number systems:
Natural numbers are counting numbers used to count objects and represent rankings. Whole numbers add 0 to represent nothing. Integers include negative numbers below 0 to represent amounts owed or temperatures below freezing. Each system builds upon the previous by adding more number types while maintaining closure under the basic arithmetic operations.
Math10 1 Lecture1
1. The document discusses basic concepts in set theory including defining sets, set operations like union and intersection, and set relationships like subsets.
2. Key concepts covered include defining a set, determining a set's cardinality, writing sets using roster and rule methods, describing relationships between sets like equivalent, disjoint, and subset, and performing common set operations.
3. Examples are provided to demonstrate set concepts like determining unions, intersections, differences, and complements of given sets.
matter in our surrounding
This document discusses the classification and properties of matter. It begins by defining matter as anything that occupies space and has mass. Matter is then classified based on physical state (solid, liquid, gas) and chemical composition (pure substances, mixtures).
The document then discusses the physical nature of matter, explaining that matter is made up of very tiny particles that have space between them and are in continuous motion. Activities are provided to demonstrate these properties.
The three states of matter - solid, liquid, gas - are defined based on properties like shape, volume, particle movement and attraction. Changes of state like melting, boiling, sublimation are explained. Factors affecting evaporation and how evaporation causes cooling are also
Work book on IRRATIONAL NUMBERS
This work book will be helpful for 9th standard students to work out problems related to the chapter IRRATIONAL NUMBERS
MB0901 QR
The document discusses key concepts relating to rational and irrational numbers including definitions, facts, formulae and procedures. It defines a rational number as a number that can be written as a ratio of integers, and an irrational number as one that cannot be written as such a ratio. Examples of procedures provided include how to locate an irrational number on the number line and how to write a recurring decimal as a ratio of integers. The document serves as a reference for important information about rational and irrational numbers for a Class 9 math curriculum.
Rational and irrartional numbers
This document defines rational and irrational numbers and discusses their properties. It states that integers and fractions are called rational numbers. Irrational numbers are numbers that cannot be written as fractions. Rational and irrational numbers together with their negatives and zero are called real numbers. It provides examples of rational and irrational numbers between 0 and 1 and notes that rational numbers can be written as repeating or terminating decimals while irrational numbers can only be approximated in decimal form. The document also includes sample math problems and their solutions.
SETS [Algebra]
The answer for:
1)Give me a group of girls whose height is > than 156 cm is E,F,G.
2) The answers for Piano and Guitar question is:
n(U) =8,
n(A)=3,
n(B)=4
(A n B) = 1
( A U B)= 6
(A U B)' = 2
Only Piano ( A - B)=2
Only guitar(B-A) =3
Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp.
Content-
Venn diagram,
Set builder(Rule method),
List method(Roster method),
Universal set,
Union of sets,
Intersection of set
Realnumbers
The real number system consists of two kinds of numbers: rational numbers and irrational numbers. Rational numbers include integers like counting numbers, whole numbers, and their opposites, as well as fractions that can be written as a ratio of two integers. Irrational numbers are any real numbers that cannot be expressed as a ratio of integers, and are therefore non-repeating and non-terminating decimals like pi.
Don't FAL out; Techno IN! Classifying Rational & Irrational Numbers
Don't FAL out; Techno IN! Classifying Rational & Irrational NumbersNorth Carolina Association for Middle Level Education
This document outlines a formative assessment lesson on classifying rational and irrational numbers. The lesson includes a pre-test to assess students' current understanding, followed by instruction on different representations of rational and irrational numbers. Students then work in small groups to categorize sample numbers. A whole-class discussion addresses questions from the pre-test and activity. Finally, students take a post-test to evaluate what they have learned about classifying rational and irrational numbers.Maths project
Euclid's Division Lemma states that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where 0 ≤ r < b. An algorithm is a series of well-defined steps to solve a problem. The word algorithm comes from the name of mathematician al-Khwarizmi. Euclid's algorithm uses the division lemma to find the highest common factor (HCF) of two integers by repeatedly dividing the larger number by the smaller number.
Real Numbers - Proofs based on irrational numbers for Class 10th maths.
Real Numbers - Proofs based on irrational numbers for Class 10th maths.Lets tute is an online learning centre. We provide quality education for all learners and 24/7 academic guidance through E-tutoring. Our Mission- Our aspiration is to be a renowned unpaid school on Web-World.
NUMBER SYSTEM
This document discusses different types of number systems. It begins by introducing natural numbers, which are counting numbers formed by repeated addition of 1. Whole numbers include all natural numbers and 0. Integers extend whole numbers infinitely in both the positive and negative directions. Rational numbers are numbers that can be written as fractions p/q where p and q are integers. Irrational numbers have non-repeating decimal expansions and cannot be written as fractions. Real numbers include all rational and irrational numbers and are represented on the number line. Methods for finding rational numbers between two given numbers and representing different types of numbers on the number line are also described.
World of matter for class 9
Matter is anything that occupies space and has mass. It is composed of small particles that are in constant motion and hold together through chemical bonds. The amount of empty space between particles determines the state of matter, with solids having the least empty space and gases having the most. Changing the temperature of matter affects the motion and bonding of its particles, allowing it to change states between solid, liquid, and gas through processes like melting, freezing, evaporation, and condensation.
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.
Viewers also liked (20)
Don't FAL out; Techno IN! Classifying Rational & Irrational Numbers
Don't FAL out; Techno IN! Classifying Rational & Irrational Numbers
Real Numbers - Proofs based on irrational numbers for Class 10th maths.
Real Numbers - Proofs based on irrational numbers for Class 10th maths.
Recently uploaded
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
How to Build a Module in Odoo 17 Using the Scaffold Method
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
The Diamonds of 2023-2024 in the IGRA collection
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
Wound healing PPT
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.
The History of Stoke Newington Street Names
Presented at the Stoke Newington Literary Festival on 9th June 2024
www.StokeNewingtonHistory.com
PCOS corelations and management through Ayurveda.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
তাই একজন নাগরিক হিসাবে এই তথ্য গুলো আপনার জানা প্রয়োজন ...।
বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
Main Java[All of the Base Concepts}.docx
This is part 1 of my Java Learning Journey. This Contains Custom methods, classes, constructors, packages, multithreading , try- catch block, finally block and more.
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptxMohd Adib Abd Muin, Senior Lecturer at Universiti Utara Malaysia
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama UniversityAkanksha trivedi rama nursing college kanpur.
Natural birth techniques are various type such as/ water birth , alexender method, hypnosis, bradley method, lamaze method etcLeveraging Generative AI to Drive Nonprofit Innovation
In this webinar, participants learned how to utilize Generative AI to streamline operations and elevate member engagement. Amazon Web Service experts provided a customer specific use cases and dived into low/no-code tools that are quick and easy to deploy through Amazon Web Service (AWS.)
Recently uploaded (20)
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...
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Build a Module in Odoo 17 Using the Scaffold Method
How to Setup Warehouse & Location in Odoo 17 Inventory
How to Setup Warehouse & Location in Odoo 17 Inventory
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
বাংলাদেশ অর্থনৈতিক সমীক্ষা (Economic Review) ২০২৪ UJS App.pdf
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
NEWSPAPERS - QUESTION 1 - REVISION POWERPOINT.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Pengantar Penggunaan Flutter - Dart programming language1.pptx
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Natural birth techniques - Mrs.Akanksha Trivedi Rama University
Leveraging Generative AI to Drive Nonprofit Innovation
Leveraging Generative AI to Drive Nonprofit Innovation
Classifying Numbers
- 1. Classifying Numbers Rational Numbers vs. Irrational Numbers
- 2. A Rational Number: An Irrational Number: • Cannot be written as a simple fraction • Non-terminating decimal (doesn’t end) • Non-repeating decimal (doesn’t repeat in a pattern) Irrational doesn’t mean that it’s crazy! 2
- 3. Examples of Rational Numbers Click on each number to see explanation Can be Can be Can be written as written as written as 7/1000 3/1 3/2 Repeating Already in decimal. Can fraction form be written as Can be 1/9 written as 4 and as 4/1 3
- 4. Examples of Irrational Numbers 4
- 5. More Irrational Numbers Click on each number to see explanation Remember . . . Irrational numbers are non-repeating and non-terminating decimals and cannot be written as a fraction. Non-repeating decimal. Can’t be written as a fraction Non-repeating decimal. Can’t be written as fraction 5
- 6. Try this . . . 6
- 7. Time to practice INCORRECT 0.5 can be written as ½ and so it is rational. Try again! Correct! 0.5 can be written as ½ Good work! 7
- 8. Time to practice 8
- 9. Time to practice CORRECT! -5.060715… non-repeating, non- terminating decimal Good job! INCORRECT -5.060715… appears to be a non- repeating, non- terminating decimal Try again! 9
- 10. Time to practice 10
- 11. Time to practice INCORRECT 2/3 is a fraction and so it is rational. Try again! CORRECT 2/3 is a fraction. Good work! 11
- 12. Time to practice 12
- 13. How many RATIONAL numbers can you find? Find the answer on the next slide 13
- 14. Did you find 6 rational numbers? They are: 14