Real numbers
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1. The document defines and provides examples of different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. 2. Key definitions include natural numbers being positive whole numbers starting at 1, whole numbers including zero, integers including positive and negative numbers on the number line, rational numbers being fractions, and irrational numbers being non-terminating and non-repeating numbers. 3. The document also presents the Fundamental Theorem of Arithmetic and Euclid's Division Lemma, with the former stating every composite number can be uniquely expressed as a product of prime numbers and the latter relating integers a and b using the division algorithm.
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This document provides an overview of different number systems including natural numbers, whole numbers, integers, and rational numbers. It begins with definitions of each number type and examples of how they are represented on a number line. An activity is described where students classify random numbers into the different categories. Rational numbers between two other rationals are discussed, as well as equivalent rational number representations. The document concludes with sample multiple choice questions to assess understanding.
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Euclid's division algorithm provides a method to compute the highest common factor (HCF) of two integers. It works by repeatedly using the division lemma to divide the larger number by the smaller number, with the remainder becoming the new smaller number, until the remainder is zero. The divisor at this final step is the HCF. The algorithm works because the HCF is preserved as the numbers are broken down through the repeated divisions. The example demonstrates finding the HCF of 455 and 42 to be 7 using this method.
Real numbers - Euclid’s Division Lemma for class 10th/grade X Maths 2014
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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
EUCLID'S DIVISION LEMMA
This document provides instructions for an activity to find the highest common factor (HCF) of two numbers experimentally based on Euclid's division lemma. The activity involves cutting strips of cardboard of different lengths to represent numbers, covering them in different colored paper, and arranging them according to the divisions in Euclid's lemma to visually demonstrate the HCF. Figures are provided to show how the strips should be arranged. The HCF is found to be the length of the final remaining strip. Observations of actual measurements are to be recorded to determine the HCF of the original two numbers.
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Real numbers - Euclid’s Division Algorithm for class 10th/grade X maths 2014
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This document defines different types of numbers and rational numbers. It explains that rational numbers can be expressed as a ratio of two integers in the form p/q, where p and q are integers and q is not zero. Examples of rational numbers include 1/2, 4/3, and 5/7. The document also discusses how rational numbers can be represented on a number line between integers, with an example given between 0 and 1. Properties of rational numbers are listed, including closure, commutative, and associative properties as well as additive identity and inverse.
[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.
Mathematics Real Numbers PPT.pptx
The group members are Aaryan Lal Das, Aryan Rai, Aakriti Lama, Pooja Gupta, Chaitanya Bajla, and Tanvi Chand. They created a mathematics project defining different types of numbers. Real numbers include rational and irrational numbers, and can be positive or negative. Rational numbers are numbers that can be expressed as a quotient of two integers. Integers are whole numbers that can be positive, negative or zero. Natural numbers are the positive integers from 1 to infinity. Whole numbers include natural numbers and zero. Irrational numbers cannot be expressed as a quotient of two integers. The addition rule is to keep the sign of the larger number when adding numbers with the same sign
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Real numbers
- 1. CH = 1
- 2. Natural Numbers The positive counting numbers starting from 1 not including zero are called Natural Numbers These are denoted by ‘N’ Letter 21 22 23 24 ………. All are Natural Numbers
- 3. Whole Numbers All the natural numbers including zero [0] are called Whole Numbers These are denoted by letter ‘W’ 10 11 12 …… All are Whole Numbers
- 4. Integers All positive & negative numbers which can be represented on number line are called Integers We can say that integers are set of natural numbers & their opposites & zero These are denoted by letter ‘Z’ {…,-3, -2, -1, 0, 1, 2, 3,…}
- 6. Rational Numbers q p The numbers which can be written in the form where p & q are integers ; q ≠ 0 are called Rational numbers They can be expressed as Terminating & Non - Terminating Repeating Numbers Examples -> 1. 56345467.39472348793 2. 90347809732.453653643 3. 3247034729387403847923748039247982374923 4. 6666.66 5. 0.00000000000003 6. 200 7. 19.1 ETC. ______________ ___
- 7. Irrational Numbers The Non Terminating & Non Repeating Numbers are called Irrational Numbers These Numbers cannot be expressed in the form q p Examples -> 1. π 2. 1.01001001000………. 3. 5454.112123123412345…….. 4. 74354354534.313323333343353363……… ETC.
- 8. Real Numbers The sum of all Rational & Irrational numbers is called Real Numbers It is denoted by letter ‘R’
- 9. Relation between Real, Rational ,Irrational ,Natural ,Whole Numbers & Integers
- 11. Fundamental Theorem Of Arithmetic (FTA) This States That -> ‘ Every Composite No. can be expressed as product of its prime numbers and this expression is unique , apart from the order in which prime factors occur ’
- 13. Euclid’s Division Lemma It states that -> ‘ For any 2 positive integers a & b there exists 2 unique integers q & r which satisfies that -> a = b*q + r , 0 < r < b & b < a ’__
- 15. Prepared By -> BHAVYAM ARORA Class = Tenth ‘A’ Roll No. = 37