Rational and irrational numbers
•Download as PPTX, PDF•
20 likes•10,378 views
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.
Report
Share
Report
Share
Recommended
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.
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.
Square and square roots
This document provides an overview of squaring numbers and finding square roots. It discusses key concepts such as:
- Squaring a number means multiplying a number by itself
- Perfect squares are numbers that can be written as the square of a whole number
- The square root of a number is another number that, when multiplied by itself, equals the original number
- Examples are provided of finding the square of numbers and the square roots of perfect squares.
Linear equtions with one variable
The document discusses equations and how to solve them. It defines an equation as a statement where two algebraic expressions are equal. It also defines a linear equation as one involving only one variable.
It then lists the four properties of equations: adding/subtracting the same quantity to both sides, multiplying/dividing both sides by the same quantity.
Next, it provides examples of how to solve different types of equations (those involving addition, subtraction, multiplication, or division of the variable) using both the traditional method of operations and the shortcut method of transposing terms.
Finally, it gives examples of solving equations with variables on both sides, word problems involving equations, and equations from applied contexts like age.
Decimals
The document discusses decimals and their relationship to fractions. It explains that decimals extend the place value system to include values less than one. The value of each place decreases by a factor of ten as you move to the right of the decimal point. Decimals can be added, subtracted, multiplied and divided using standard algorithms. Terminating decimals can be converted to fractions by writing the decimal as the numerator over an appropriate power of ten as the denominator. Repeating decimals can be converted to fractions by writing the repeating portion as the numerator over nines and zeros in the denominator.
Hcf+lcm
This document discusses highest common factors (HCF) and lowest common multiples (LCM). It defines multiples as numbers divisible by another with no remainder. Common multiples contain each number a number of times. The lowest common multiple is the smallest number divisible by all numbers. To find the LCM, list multiples and find the lowest number common to all lists. Similarly, factors divide a number with no remainder, and the highest common factor is the largest number dividing all numbers. The document provides examples of finding HCF and LCM.
Congruence of triangles
This document discusses congruence of triangles, which is when two triangles have the same shape and size, meaning one triangle can be repositioned to coincide precisely with the other. It provides examples of congruent and non-congruent triangles based on equal angles and side lengths. The key properties for congruence of triangles are that they must have equal measures of angles and equal lengths of sides.
Variable and Algebraic Expressions
1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.
Recommended
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.
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.
Square and square roots
This document provides an overview of squaring numbers and finding square roots. It discusses key concepts such as:
- Squaring a number means multiplying a number by itself
- Perfect squares are numbers that can be written as the square of a whole number
- The square root of a number is another number that, when multiplied by itself, equals the original number
- Examples are provided of finding the square of numbers and the square roots of perfect squares.
Linear equtions with one variable
The document discusses equations and how to solve them. It defines an equation as a statement where two algebraic expressions are equal. It also defines a linear equation as one involving only one variable.
It then lists the four properties of equations: adding/subtracting the same quantity to both sides, multiplying/dividing both sides by the same quantity.
Next, it provides examples of how to solve different types of equations (those involving addition, subtraction, multiplication, or division of the variable) using both the traditional method of operations and the shortcut method of transposing terms.
Finally, it gives examples of solving equations with variables on both sides, word problems involving equations, and equations from applied contexts like age.
Decimals
The document discusses decimals and their relationship to fractions. It explains that decimals extend the place value system to include values less than one. The value of each place decreases by a factor of ten as you move to the right of the decimal point. Decimals can be added, subtracted, multiplied and divided using standard algorithms. Terminating decimals can be converted to fractions by writing the decimal as the numerator over an appropriate power of ten as the denominator. Repeating decimals can be converted to fractions by writing the repeating portion as the numerator over nines and zeros in the denominator.
Hcf+lcm
This document discusses highest common factors (HCF) and lowest common multiples (LCM). It defines multiples as numbers divisible by another with no remainder. Common multiples contain each number a number of times. The lowest common multiple is the smallest number divisible by all numbers. To find the LCM, list multiples and find the lowest number common to all lists. Similarly, factors divide a number with no remainder, and the highest common factor is the largest number dividing all numbers. The document provides examples of finding HCF and LCM.
Congruence of triangles
This document discusses congruence of triangles, which is when two triangles have the same shape and size, meaning one triangle can be repositioned to coincide precisely with the other. It provides examples of congruent and non-congruent triangles based on equal angles and side lengths. The key properties for congruence of triangles are that they must have equal measures of angles and equal lengths of sides.
Variable and Algebraic Expressions
1. The document provides examples and explanations for evaluating algebraic expressions by substituting values for variables.
2. It gives examples of evaluating expressions involving addition, subtraction, multiplication, division, and order of operations.
3. Students are asked to evaluate expressions for given variable values to check their understanding.
Linear Equation In one variable class 7
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.
Squares & square roots - class 8th
It is a school project on mathematics chapter of class 8th in which every thing is explained briefly. Made by - Sana Rajar
Basics about exponents
Exponents are used to represent repeated multiplication of a number, called the base. The exponent indicates how many times the base is multiplied. Some key laws for exponents include: when multiplying the same bases, add the exponents; when dividing the same bases, subtract the exponents; when raising a power to another power, multiply the exponents. Exponents provide a shorthand way to write very large or small numbers.
Powers and Exponents
The document discusses powers and exponents. It explains that multiplication is a shortcut for repeated addition, and exponents are a shortcut for repeated multiplication. An exponent written as a base number with a little number on top, where the base is the number being multiplied and the exponent tells how many times to multiply the base by itself. Common mistakes in working with exponents are also described.
Integers Class 6
The document discusses integers and their properties. It defines integers as the collection of whole numbers and their negatives, with zero being neither positive nor negative. Integers can be represented on a number line. The key operations with integers are addition and subtraction, which follow specific rules depending on the signs of the integers being operated on. For example, adding two positives simply adds the numbers, while adding a positive and negative integer subtracts the numbers and takes the sign of the larger integer ignoring signs.
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.
Exponent, mathematics 7
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
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.
Types of numbers
The document defines and provides examples of different types of numbers:
Natural numbers start at 1 and do not include 0. Whole numbers include all natural numbers and 0. Even numbers are divisible by 2, while odd numbers are not. Prime numbers are only divisible by 1 and themselves, while composite numbers can be divided by other numbers.
Multiplication and division of fractions
This document contains lesson materials on operations with fractions, including examples of addition, subtraction, multiplication, and division of fractions. It provides steps for solving each type of operation, such as multiplying the numerators and denominators for multiplication, or applying cross multiplication for division. It then includes practice problems for students to work through, covering adding and subtracting similar and dissimilar fractions, as well as multiplying and dividing fractions. The document aims to teach students the key steps and methods for performing different mathematical operations with fractions.
Simple Equations I
This document discusses solving one-step linear equations using addition and subtraction. It defines key terms like equations, solutions, and isolating variables. It explains that when transforming equations, the same operations must be applied to both sides to maintain equivalence. Inverse operations like addition and subtraction can isolate variables. Examples show how to isolate variables using addition or subtraction and solve equations. Students are then prompted to solve practice equations on their own. The document also discusses using equations to solve real-world problems, like finding a person's maximum heart rate based on their age.
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.
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.
Ratio powerpoint
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Mat_5th_UD1_Fractions_Presentation
This document defines fractions and their key elements. It explains that a fraction represents a part of a whole, with the numerator indicating the parts and the denominator indicating the total parts of the whole. It describes how to represent fractions on a number line and compare fractions based on their numerators and denominators. Finally, it relates fractions to units and division, noting how fractions below, equal to, or above one unit can be represented as exact or non-exact divisions.
Lines And Angles
This document defines and explains various geometric terms including:
- Point, line, line segment, ray
- Types of angles such as acute, obtuse, right
- Relationships between angles such as adjacent, vertical, complementary, supplementary
- Properties of angles and lines cut by a transversal, including corresponding angles, alternate angles, and interior angles
- Theorems regarding the sum of angles formed when a ray stands on a line, vertically opposite angles, parallel lines cut by a transversal, and lines parallel to the same line.
Square roots
This document provides information about square roots and real numbers. It includes:
1) Examples of finding square roots of perfect squares and estimating other square roots.
2) Classifying different types of real numbers such as rational numbers, irrational numbers, integers, natural numbers, and more.
3) Examples of classifying given numbers as rational, irrational, integers, and other categories.
cubes and cube root
The document discusses cubes and cube roots. A cube is a three-dimensional solid shape where all sides are equal. The cube of a number is when that number is multiplied by itself three times. A perfect cube is a number that can be written as the cube of another number, such as 1, 8, 27, 64, 125 and so on. The cube root of a perfect cube will be an integer, while the cube root of a non-perfect cube may need to be simplified by factoring the number into terms with a cube root of an integer. Examples of simplifying cube roots and finding cube roots of perfect and non-perfect cubes are provided.
algebraic expression
This document provides an overview of algebraic expressions and identities. It defines terms, factors, coefficients, monomials, binomials, polynomials, like and unlike terms. It explains how to perform addition, subtraction, multiplication, and division of algebraic expressions. It also defines what an identity is and how to apply identities.
Exponents and power
The document discusses exponents and powers in mathematics. It defines key terms like base, exponent, and power. It provides examples of exponents like 22 = 4 (two squared) and 23 = 8 (two cubed). It notes rules for exponents like when the exponent is 1 the number is the same as the base, and when the exponent is 0 the answer is 1 except for when the base is 0. The document also discusses properties of exponents like product of powers, power to a power, power of product, and addition/multiplication of exponents.
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 denominators must first be made equal by finding the lowest common denominator. 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.
Relations and functions
This document defines relations and functions in mathematics. A relation is a set of ordered pairs where the domain is the set of all x values and the range is the set of all y values. A function assigns each element in the domain (set of x values) to exactly one element in the range (set of y values). Functions are commonly represented by letters like f(x), where f denotes the name of the function and x is the variable. The left side of a function equation tells us the name and variable of the function, not that the function is being multiplied.
More Related Content
What's hot
Linear Equation In one variable class 7
This document defines and provides examples of linear equations in one variable. It explains that a linear equation is an equation that can be written in the form ax + b = c or ax = b, where a, b, c are constants and a ≠ 0. Examples of linear equations given include 3x + 9 = 0 and 7x + 5 = 2x - 9. The document also discusses how to determine if a value is a solution to a linear equation by substitution and simplification. Steps for solving linear equations are provided, which include isolating the variable using inverse operations like addition/subtraction and multiplication/division.
Squares & square roots - class 8th
It is a school project on mathematics chapter of class 8th in which every thing is explained briefly. Made by - Sana Rajar
Basics about exponents
Exponents are used to represent repeated multiplication of a number, called the base. The exponent indicates how many times the base is multiplied. Some key laws for exponents include: when multiplying the same bases, add the exponents; when dividing the same bases, subtract the exponents; when raising a power to another power, multiply the exponents. Exponents provide a shorthand way to write very large or small numbers.
Powers and Exponents
The document discusses powers and exponents. It explains that multiplication is a shortcut for repeated addition, and exponents are a shortcut for repeated multiplication. An exponent written as a base number with a little number on top, where the base is the number being multiplied and the exponent tells how many times to multiply the base by itself. Common mistakes in working with exponents are also described.
Integers Class 6
The document discusses integers and their properties. It defines integers as the collection of whole numbers and their negatives, with zero being neither positive nor negative. Integers can be represented on a number line. The key operations with integers are addition and subtraction, which follow specific rules depending on the signs of the integers being operated on. For example, adding two positives simply adds the numbers, while adding a positive and negative integer subtracts the numbers and takes the sign of the larger integer ignoring signs.
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.
Exponent, mathematics 7
After this presentation students will be able to define
Identify Base, Exponents/Indices, value
Laws of Exponents/Indices
Product law
Quotient law
Power law
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.
Types of numbers
The document defines and provides examples of different types of numbers:
Natural numbers start at 1 and do not include 0. Whole numbers include all natural numbers and 0. Even numbers are divisible by 2, while odd numbers are not. Prime numbers are only divisible by 1 and themselves, while composite numbers can be divided by other numbers.
Multiplication and division of fractions
This document contains lesson materials on operations with fractions, including examples of addition, subtraction, multiplication, and division of fractions. It provides steps for solving each type of operation, such as multiplying the numerators and denominators for multiplication, or applying cross multiplication for division. It then includes practice problems for students to work through, covering adding and subtracting similar and dissimilar fractions, as well as multiplying and dividing fractions. The document aims to teach students the key steps and methods for performing different mathematical operations with fractions.
Simple Equations I
This document discusses solving one-step linear equations using addition and subtraction. It defines key terms like equations, solutions, and isolating variables. It explains that when transforming equations, the same operations must be applied to both sides to maintain equivalence. Inverse operations like addition and subtraction can isolate variables. Examples show how to isolate variables using addition or subtraction and solve equations. Students are then prompted to solve practice equations on their own. The document also discusses using equations to solve real-world problems, like finding a person's maximum heart rate based on their age.
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.
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.
Ratio powerpoint
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Mat_5th_UD1_Fractions_Presentation
This document defines fractions and their key elements. It explains that a fraction represents a part of a whole, with the numerator indicating the parts and the denominator indicating the total parts of the whole. It describes how to represent fractions on a number line and compare fractions based on their numerators and denominators. Finally, it relates fractions to units and division, noting how fractions below, equal to, or above one unit can be represented as exact or non-exact divisions.
Lines And Angles
This document defines and explains various geometric terms including:
- Point, line, line segment, ray
- Types of angles such as acute, obtuse, right
- Relationships between angles such as adjacent, vertical, complementary, supplementary
- Properties of angles and lines cut by a transversal, including corresponding angles, alternate angles, and interior angles
- Theorems regarding the sum of angles formed when a ray stands on a line, vertically opposite angles, parallel lines cut by a transversal, and lines parallel to the same line.
Square roots
This document provides information about square roots and real numbers. It includes:
1) Examples of finding square roots of perfect squares and estimating other square roots.
2) Classifying different types of real numbers such as rational numbers, irrational numbers, integers, natural numbers, and more.
3) Examples of classifying given numbers as rational, irrational, integers, and other categories.
cubes and cube root
The document discusses cubes and cube roots. A cube is a three-dimensional solid shape where all sides are equal. The cube of a number is when that number is multiplied by itself three times. A perfect cube is a number that can be written as the cube of another number, such as 1, 8, 27, 64, 125 and so on. The cube root of a perfect cube will be an integer, while the cube root of a non-perfect cube may need to be simplified by factoring the number into terms with a cube root of an integer. Examples of simplifying cube roots and finding cube roots of perfect and non-perfect cubes are provided.
algebraic expression
This document provides an overview of algebraic expressions and identities. It defines terms, factors, coefficients, monomials, binomials, polynomials, like and unlike terms. It explains how to perform addition, subtraction, multiplication, and division of algebraic expressions. It also defines what an identity is and how to apply identities.
Exponents and power
The document discusses exponents and powers in mathematics. It defines key terms like base, exponent, and power. It provides examples of exponents like 22 = 4 (two squared) and 23 = 8 (two cubed). It notes rules for exponents like when the exponent is 1 the number is the same as the base, and when the exponent is 0 the answer is 1 except for when the base is 0. The document also discusses properties of exponents like product of powers, power to a power, power of product, and addition/multiplication of exponents.
What's hot (20)
Viewers also liked
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 denominators must first be made equal by finding the lowest common denominator. 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.
Relations and functions
This document defines relations and functions in mathematics. A relation is a set of ordered pairs where the domain is the set of all x values and the range is the set of all y values. A function assigns each element in the domain (set of x values) to exactly one element in the range (set of y values). Functions are commonly represented by letters like f(x), where f denotes the name of the function and x is the variable. The left side of a function equation tells us the name and variable of the function, not that the function is being multiplied.
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.
Relations and Functions
The document defines relations and functions. A relation is a set of ordered pairs, while a function is a special type of relation where each x-value is mapped to only one y-value. The domain is the set of x-values and the range is the set of y-values. Functions can be identified using the vertical line test or by mapping the relation to check if any x-values are mapped to multiple y-values. Evaluating functions involves substituting domain values into the function rule to find the corresponding range values.
Relations and functions (Mariam)
The document discusses functions and relations. It defines a function as a set of ordered pairs where each x-value is paired with only one y-value. A relation is a function only if each x-value is paired with exactly one y-value; if an x-value is paired with more than one y-value, it is not a function. It then asks the reader to identify which of several relations presented are functions based on this definition. It also gives some examples of evaluating simple functions.
Math functions, relations, domain & range
This document discusses math functions, relations, and their domains and ranges. It provides examples of relations and explains that the domain is the set of first numbers in ordered pairs, while the range is the set of second numbers. A function is defined as a relation where each x-value has only one corresponding y-value. It compares examples of relations that are and are not functions and describes how to evaluate functions by inserting values. Tests for identifying functions like the vertical line test are also outlined.
Relations and Functions (Algebra 2)
Students learn about relations and functions, and the vertical line test.
Students also learn to evaluate functions
Viewers also liked (7)
Similar to Rational and irrational numbers
Mathematics class 8
Rational numbers include integers, fractions, and numbers that can be expressed as a ratio of two integers, like p/q. Rational numbers can be positive or negative depending on whether the numerator and denominator have the same or different signs. Any rational number can be expressed in its standard form by dividing the numerator and denominator by their greatest common factor.
Maths
The document discusses different types of numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Natural numbers are the counting numbers from 1 to infinity. Whole numbers include zero and all natural numbers. Integers include whole numbers and their negatives. Real numbers include all rational numbers like integers and fractions as well as irrational numbers like the square root of 2. Rational numbers can be written as fractions while irrational numbers cannot. A number line can represent all these different types of numbers.
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.
Maths project (number line)
maths project useful for 7th to 9th std. For NCERT school project on number line. More description on number line.
Real basic define arivu
This document defines basic number types including real numbers, rational numbers, irrational numbers, complex numbers, natural numbers, whole numbers, integers, and their subsets. Real numbers include all integers and rational/irrational numbers. Rational numbers can be expressed as p/q ratios of integers, while irrational numbers cannot. Complex numbers are numbers of the form a + ib, where a and b are real and i is the imaginary unit.
ch-1rationalnumbers-201017103609.pdf
Rational numbers include all integers as well as numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication but not division. They have identities and inverses. Rational numbers can be represented on a number line and there are an infinite number of rational numbers between any two given rational numbers, found using methods like the equivalent fractions method or mean method.
Rational Numbers
Rational numbers include all integers as well as numbers that can be expressed as fractions p/q where p and q are integers and q is not equal to 0. Rational numbers are closed under addition, subtraction, and multiplication but not division. They have identities and inverses. Rational numbers can be represented on a number line and there are infinite numbers between any two rational numbers that can be found using methods like the mean or equivalent fractions.
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.
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.
MATH; discussion_20240304_113651_0000.pdf
This document provides information about comparing different types of numbers on a number line, including integers, fractions, decimals, and whole numbers. It discusses key topics like:
1. Using a number line to compare integers with other numbers like whole numbers, fractions, and decimals.
2. Identifying positive and negative integers.
3. Solving word problems that involve comparing integers to other number types on a number line.
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.
Number systems
This document provides an overview of different number systems:
1. It defines six types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers.
2. Natural numbers are used for counting and start at 1. Whole numbers are natural numbers with 0 included. Integers include whole numbers and their negatives.
3. Rational numbers can be written as fractions with integer numerators and denominators. Irrational numbers cannot be written as fractions with integers and have non-repeating decimals.
4. Real numbers include all rational and irrational numbers.
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.
[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.
Numeros reales [autoguardado]
The document discusses real numbers and their properties. It defines real numbers as all numbers that can be represented on the number line, including both rational and irrational numbers. It classifies real numbers as rational, irrational, integers, natural numbers, and discusses their characteristics and properties. It also covers operations with real numbers like addition, subtraction, multiplication, division, powers and roots. Finally, it discusses intervals of real numbers and operations between intervals.
math 11.pptx
Real numbers include any number that can be found in the real world, such as natural numbers, integers, rational numbers like fractions, and irrational numbers like the square root of numbers. Real numbers are represented by the symbol R and are the union of rational numbers Q and irrational numbers Ǭ. Examples of real numbers include integers, fractions, the square root of 5, and irrational numbers like pi, while complex numbers like √-1 are non-real numbers.
Rational Numbers
Rational Numbers PPT for Class VIII, Properties of Rational Numbers: Commutative, Distributive, Associative, etc.
402 Master of arts in teaching Math second Sem. .pptx
A Report in Mathematics 402 in my masteral Class
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.
Number system
about all types of numbers such as rational numbers, real numbers,irrational numbers,integers,whole numbers, natural numbers etc
Similar to Rational and irrational numbers (20)
402 Master of arts in teaching Math second Sem. .pptx
402 Master of arts in teaching Math second Sem. .pptx
Recently uploaded
Introduction to AI for Nonprofits with Tapp Network
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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.
Advanced Java[Extra Concepts, Not Difficult].docx
This is part 2 of my Java Learning Journey. This contains Hashing, ArrayList, LinkedList, Date and Time Classes, Calendar Class and more.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar KanvariaHow to Fix the Import Error in the Odoo 17
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
clinical examination of hip joint (1).pdf
described clinical examination all orthopeadic conditions .
A Strategic Approach: GenAI in Education
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Digital Artifact 1 - 10VCD Environments Unit
Digital Artifact 1 - 10VCD Environments Unit - NGV Pavilion Concept Design
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.
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...National Information Standards Organization (NISO)
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance
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.
How to Manage Your Lost Opportunities in Odoo 17 CRM
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Add Chatter in the odoo 17 ERP Module
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
Recently uploaded (20)
Introduction to AI for Nonprofits with Tapp Network
Introduction to AI for Nonprofits with Tapp Network
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
The simplified electron and muon model, Oscillating Spacetime: The Foundation...
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Chapter 4 - Islamic Financial Institutions in Malaysia.pptx
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
Pollock and Snow "DEIA in the Scholarly Landscape, Session One: Setting Expec...
A Survey of Techniques for Maximizing LLM Performance.pptx
A Survey of Techniques for Maximizing LLM Performance.pptx
Liberal Approach to the Study of Indian Politics.pdf
Liberal Approach to the Study of Indian Politics.pdf
How to Manage Your Lost Opportunities in Odoo 17 CRM
How to Manage Your Lost Opportunities in Odoo 17 CRM
Rational and irrational numbers
- 1. HOLIDAY HOMEWORK 1 SUBMITTED BY- LAKSHMI SINGH SUBMITTED TO-
- 2. 2
- 3. RATIONAL NUMBERS A rational number is a number that can be written in the form p/q , where p and q are integers and q is not equal to 0. EXAMPLES- 2/5, -3/4 The collection of numbers in the form of p/q, where q ≠ 0, is represented by Q. 3 Rational numbers include natural numbers, whole numbers, integers and all negative and positive fractions.
- 4. TYPES OF RATIONAL NUMBERS Positive rational number Rational number is positive if its numerator and denominator are both either positive integers or negative integers. Eg : 2/5 , -8/-5. Negative rational number If either the numerator or the denominator of a rational number is a negative integer ,then the rational number is called a negative rational number. Eg: -2/5 Standard form A rational number is said to be in its standard form if its numerator and denominator have no common factor other than 1,and its denominator is a positive integer . Eg: 4/7 4
- 5. 5Representation of Rational Numbers on the Number Line To express rational numbers appropriately on the number line, divide each unit length into as many number of equal parts as the denominator of the rational number and then mark the given number on the number line.
- 6. OPERATION ON RATIONAL NUMBERS 6 1. ADDITION OF RATIONAL NUMBERS To add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators NOTE: To add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators
- 7. 2. SUBTRACTION OF RATIONAL NUMBERS Subtraction is the inverse operation of addition. To subtract rational numbers that have a common denominator, we subtract the numerator, but we do not subtract the denominators. 7
- 8. 3. MULTIPLYING TWO RATIONAL NUMBERS To multiply two rational numbers, we multiply the numerators to get the new numerator and multiply the denominators to get the new denominator 4. DIVISION OF TWO RATIONAL NUMBERS 8
- 9. IRRATIONAL NUMBERS An irrational number is any real number that cannot be expressed as a ratio a/b, where a and b are integers, with b non-zero, and therefore not a rational number. All numbers which cannot be written as an integer upon integer where the denominator is zero and both integers are co-primes are irrational numbers. They are non - terminating non-repeating decimal expansions. The roots of prime number are irrational. 9
- 10. EXAMPLES OF IRRATIONAL NUMBERS 𝜋 = 3.1415926535897932384626433 e= 2.71828182845904523536 2 =1.41421356237309504 3 =1.732050807568877293527 10
- 11. 11