9.2 rational and irrational numbers day 1
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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.
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This is meant for age group 11 to 14 years.
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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
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The document discusses various math concepts related to fractions, decimals, and percents including:
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ppt on matter in our surroundings
This document is a school project on matter and its states by a 9th grade student named Jyoti Kumari. It defines matter as anything that has mass and takes up space, and discusses the three states of matter - solid, liquid, and gas. It explains the characteristics of each state in terms of intermolecular forces and kinetic energy of particles. The document also covers topics like temperature, the units used to measure it, melting point, boiling point, evaporation, the factors that affect evaporation, and some sample questions related to these concepts.
Ppt matter in our surroundings
It is a ppt based on Matter in our surroundings
It is a good way to learn about matter and its states like photos , explanations , etc .
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Don't FAL out; Techno IN! Classifying Rational & Irrational Numbers
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Matter in our surroundings for class 9 to understand better!!!!!!
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Introduction
This document provides an overview of key concepts in mathematics including:
1) It describes the aims of the Mathematics 1 module which are to reinforce basic numeracy and algebraic manipulation through lectures, seminars and tutorials.
2) It covers various topics in numbers such as place value, real numbers, rational numbers, integers, and properties of number systems.
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This document introduces different types of numbers. Real numbers include all numbers that can be expressed as decimals, and are divided into rational and irrational numbers. Rational numbers can be written as fractions with integer numerators and denominators not equal to zero, such as repeating decimals. Irrational numbers cannot be written as fractions, such as roots of non-perfect squares. The document provides examples of rational numbers like fractions and repeating decimals, as well as irrational numbers like pi. It also discusses how rational numbers include natural numbers, whole numbers, and integers.
The-Real-Number-System.ppt
The real numbers are the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line. There are infinitely many real numbers just as there are infinitely many in the other sets of numbers.
Weeks idol power_pointtranscript
The document discusses the classification of numbers in the real number system. It describes rational numbers as numbers that can be written as fractions with integer numerators and non-zero denominators, including integers. Rational numbers can be expressed with terminating or repeating decimals. Irrational numbers cannot be expressed as fractions and their decimal representations do not terminate or repeat. The real number system consists of both rational numbers, such as integers and numbers with terminating or repeating decimals, and irrational numbers like π.
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[L1] NUMBER SYSTEM (6).pdf
Surabhi Gangwar has over 6 years of teaching experience and has mentored over 10,000 students, including 5,000 students for NTSE and Olympiad exams. She provides lessons on topics related to number systems, including natural numbers, whole numbers, integers, fractions, irrational numbers, real numbers, and rational numbers. She explains their properties and provides examples of representing them on a number line.
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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.
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.
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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.
E resorce
This document provides an introduction to irrational numbers. It begins by explaining that while natural numbers were originally used to count, fractions were later needed to measure lengths and areas. Some lengths could not be expressed as fractions, and these were called irrational numbers. The document then defines rational and irrational numbers, provides some examples of irrational numbers like the square root of 2 and pi, and gives a brief history of the discovery of irrational numbers by Hippasus. It concludes by explaining how to perform operations like addition, multiplication and division with irrational numbers.
Lesson 1.10 grade 8
This document provides examples and explanations of concepts related to classifying and ordering different types of numbers:
1) It defines rational and irrational numbers, and provides examples of each. Rational numbers can be expressed as ratios of integers, while irrational numbers cannot.
2) Exercises are included for classifying numbers as rational or irrational, comparing irrational numbers on a number line, and ordering sets of numbers from least to greatest.
3) Answering "Why is it helpful to write numbers in different ways?" the document explains that not all numbers can be written the same way, like irrational numbers that cannot be expressed as integers. Being able to classify numbers facilitates understanding and operations involving different types of numbers.
Numeral System
A numeral is a sign, or figure that represents a number. It is a mathematical numbering system. In other words, A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.
Purpose:
This webinar by ASK aims to spread awareness about the practical use of the decimal number system in daily life to minimize errors and make calculations easier.
An applied approach to calculas
This chapter reviews real numbers including:
[1] Classifying numbers as natural numbers, integers, rational numbers, irrational numbers, and real numbers. Rational numbers can be written as fractions while irrational numbers cannot.
[2] Approximating irrational numbers like π as decimals to a given number of decimal places by rounding or truncating.
[3] How calculators handle decimals by either truncating or rounding values based on their display capabilities. A scientific or graphing calculator is recommended for this course.
2.7 find square roots and compare real numbers day 1
This document provides objectives and content on evaluating and approximating square roots and comparing different types of real numbers. It defines key terms like square root, radicand, radical, perfect squares, irrational numbers, and real numbers. Examples are provided to determine if a number is an integer, whole number, irrational number, or rational number. The document concludes with guided practice problems ordering numbers on a number line and determining properties of different numbers.
Tenth class state syllabus-text book-em-ap-ts-mathematics
This document discusses rational and irrational numbers. It begins by recalling rational numbers as numbers that can be written as p/q where p and q are integers and q is not equal to 0. Irrational numbers cannot be written in this form and include numbers like √2, √3, and π. Together, rational and irrational numbers make up the set of real numbers. The document then explores properties of rational numbers, such as when their decimal expansions terminate or repeat periodically. It introduces the Fundamental Theorem of Arithmetic and uses it to prove results about rational numbers and their representations as decimals.
PPT1_Rational-and-Irrational-Numbers-PowerPoint.pptx
This document discusses rational and irrational numbers. Rational numbers can be written as fractions with whole number numerators and denominators, and include terminating and repeating decimals. Irrational numbers cannot be written as fractions and are represented by non-terminating, non-repeating decimals like the square root of 2 or pi. Both rational and irrational numbers exist on the real number line, making up the set of real numbers.
2.1 integers & rational numbers
This document provides an overview of key concepts about real numbers that will be covered in Chapter 2, including:
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- How to classify numbers as integers, rational numbers, or whole numbers.
- How to compare and order rational numbers on a number line.
- Properties of opposites, absolute value, and how to evaluate conditional statements.
- Examples and practice problems are provided to illustrate these concepts.
Classifying numbers
This document provides an overview of different types of numbers: whole numbers, integers, rational numbers, and irrational numbers. It defines each type and provides examples. Whole numbers are the counting numbers including 0. Integers include both positive and negative whole numbers. Rational numbers can be written as fractions, while irrational numbers cannot be written as fractions and have non-repeating decimals. The document uses examples and diagrams to illustrate how the different number types are related and how to identify each one.
DIGITAL TEXTBOOK
This document discusses irrational numbers and rounding numbers to a certain number of decimal places. It begins by explaining that some numbers like pi or the square root of 2 cannot be written as a fraction of two integers, and are therefore considered irrational. It then provides examples of irrational numbers and explains how to identify them. The document concludes by demonstrating how to round numbers, both rational and irrational, to a specified number of decimal places through examples such as rounding pi to 4 decimal places.
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.
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2.7 find square roots and compare real numbers day 1
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The document outlines the summer schedule for the FM Girls Basketball program. It includes shooting camps, skills camps, and open gym times for different age groups from Mondays through Fridays in July. Shooting camps are offered for high school, 4th-8th grade, and 2nd-3rd grade groups. Skills camps are for 2nd-3rd and 2nd-4th graders. Open gym times are provided for high school, 5th-12th graders, and 7th/8th graders and high schoolers.
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Functions fill in the blank passage
A function is a mathematical rule that assigns each input exactly one output. Functions can be represented as ordered pairs, tables, graphs or equations. When represented as ordered pairs or tables, there cannot be repeats in the x-values, otherwise it is not a function. On a graph, if a vertical line intersects the graph more than once, it is not a function. Functions can be linear or non-linear. A linear function has a constant rate of change, while a non-linear function will have variables with exponents or multiplied together.
Functions fill in the blank passage
A function is a mathematical rule that assigns each input exactly one output. Functions can be represented as ordered pairs, tables, graphs or equations. When represented as ordered pairs or tables, there cannot be repeats in the x-values, otherwise it is not a function. On a graph, if a vertical line intersects the graph more than once, it is not a function. Functions can be linear or non-linear. A linear function has a constant rate of change, while a non-linear function does not have a straight line graph or variables with exponents or being multiplied.
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1. The function y = 7 + 3(x - 2) is linear because it can be written in the form y = mx + b, where m is the slope (3) and b is the y-intercept (7).
2. The data points (1, 12) (2,7) (3,4) (4, 3) (5, 4) define a non-linear relationship because as x increases, y does not increase or decrease at a consistent rate.
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9.2 rational and irrational numbers day 1
- 1. Write the fraction as a decimal. Lesson 9.2 , For use with pages 475-480 1. 4 5 2. 5 9
- 2. Write the fraction as a decimal. Lesson 9.2 , For use with pages 475-480 ANSWER 0.8 1. 4 5 2. 5 9 ANSWER 0.5
- 3. RATIONAL and IRRATIONAL NUMBERS 9.2
- 6. 1, 2, 3, 4, etc. 0, 1, 2, 3, 4, 5 .. –2, –1, 0, 1, 2, . Rational and irrational numbers Can be written as a fraction Can’t be written as a fraction
- 13. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 5 8 1.
- 14. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 5 8 1. Rational because if we write it in its decimal form then it would be 0.625 which is terminating so it is a rational number ANSWER
- 15. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 2.
- 16. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 2. ANSWER Irrational because it is not a perfect square 2.64579131 . . . .
- 17. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 3.
- 18. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 3. ANSWER Rational because it is a perfect square
- 19. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 4. 2 9
- 20. GUIDED PRACTICE for Example 1 Tell whether the number is rational or irrational . Explain your reasoning. 4. 2 9 ANSWER Rational because if we write it in its decimal from then it would be 0.2 where 2 repeating so it is a rational number
- 21. EXAMPLE 1 Number Rational Rational Irrational Terminating Repeating Non terminating and non repeating Classifying Real Numbers Type Decimal Form Type of Decimal a. 3 4 b. 1 11 c. 3 11 1 = 0.0909… = 0.09 3 = 1.7320508 . . . 3 4 = 0.75 3