# Chapter 1.1 properties of-real-numbers

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## Chapter 1.1 properties of-real-numbersPresentation Transcript

• Properties of Real Numbers
• __ __ ____ _ Properties of Real Numbers Vocabulary 1) real numbers 2) rational numbers 3) irrational numbers
• Classify real numbers.
• Use the properties of real numbers to evaluate expressions.
• All of the numbers that you use in everyday life are real numbers . Properties of Real Numbers
• All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers
• All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers x
• All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
• All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and every point on the number line represents one real number. Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
• All of the numbers that you use in everyday life are real numbers . Each real number corresponds to exactly one point on the number line, and every point on the number line represents one real number. Properties of Real Numbers x 0 1 2 3 4 5 -5 -4 -2 -1 -3
• Real numbers can be classified a either _______ or ________. Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational zero Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational zero The decimal form of a rational number is either a terminating or repeating decimal. Examples: ratio form decimal form Properties of Real Numbers Ratio nal numbers can be expressed as a ratio , where a and b are integers and b is not ____!
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? Properties of Real Numbers
• Real numbers can be classified a either _______ or ________. rational irrational A real number that is not rational is irrational. The decimal form of an irrational number neither __________ nor ________. terminates repeats Examples: More Digits of PI? Do you notice a pattern within this group of numbers? They’re all PRIME numbers! Properties of Real Numbers
• Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers
• Q = rationals I = irrationals Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I
• Q = rationals I = irrationals Z = integers Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I Z
• Q = rationals I = irrationals Z = integers W = wholes Relationships among the real numbers - ( sets and subsets ). Properties of Real Numbers Q I Z W
• The square root of any whole number is either whole or irrational. Properties of Real Numbers
• The square root of any whole number is either whole or irrational. Properties of Real Numbers For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
• The square root of any whole number is either whole or irrational. Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
• The square root of any whole number is either whole or irrational. Common Misconception: Do not assume that a number is irrational just because it is expressed using the square root symbol. Find its value first! Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
• The square root of any whole number is either whole or irrational. Common Misconception: Do not assume that a number is irrational just because it is expressed using the square root symbol. Find its value first! Study Tip: KNOW and recognize (at least) these numbers, Properties of Real Numbers x 0 1 3 2 4 5 6 7 9 8 10 For example, is a whole number, but , since it lies between 5 and 6, must be irrational.
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Properties of Real Numbers
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Associative Identity Inverse Distributive Properties of Real Numbers Commutative Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• The real number system is an example of a mathematical structure called a field . Some of the properties of a field are summarized in the table below: Commutative Associative Identity Inverse Distributive Properties of Real Numbers Real Number Properties For any real numbers a , b , and c . Property Addition Multiplication
• Reciprocals
• The Reciprocal of a is providing a does NOT equal 0.
• Definition of Subtraction: