Properties of Real Numbers

You'll Learn To: 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

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 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? 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

Consider these Java Applets to better understand the Distributive Property Algebra Tiles 1 Algebra Tiles 2 End of Lesson