Lesson 1.2 Real Number System and Domain Objective - To recognize different sets of numbers and to identify a domain. Sets of Numbers Naturals - Natural counting numbers { 1, 2, 3… } Wholes - Natural counting numbers and zero { 0, 1, 2, 3… } Integers - Positive or negative natural numbers or zero { … -3, -2, -1, 0, 1, 2, 3… } Rationals - Any number which can be written as a fraction Irrationals - Any decimal number which can’t be written as a fraction. A non-terminating and non-repeating decimal. Reals - Rationals irrationals Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series Algebra 1 by James Wenk © 2003 published by TEACHINGpoint

Real Numbers Rationals Irrationals 7 2.09 Examples: Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples: 7 2.09 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Repeating Decimal Pattern Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Real Numbers Rationals Irrationals 7 2.09 Examples: Examples: Any number which can be written as a fraction Non-terminating and non- repeating decimals which can’t be written as fractions. Examples: Examples: 7 2.09 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

…-3, -2, -1, 0, 1, 2, 3... …-3, -2, -1 Sets of Numbers Reals Rationals Irrationals - any number which can be written as a fraction. - non-terminating and non-repeating decimals , 7, -0.4 Fractions/Decimals Integers , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3... Negative Integers Wholes …-3, -2, -1 0, 1, 2, 3... Zero Naturals 1, 2, 3... Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Reals Make a Venn Diagram that displays the following sets of numbers: Reals, Rationals, Irrationals, Integers, Wholes, and Naturals. Reals Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals 1, 2, 3... Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Reals Imaginary Numbers Rationals -2.65 Integers -3 -19 Wholes Irrationals Naturals 1, 2, 3... Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) -6 Integer, Rational, Real 2) Rational, Real 3) 14 Natural, Whole, Integer, Rational, Real 4) 6 Irrational, Real Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3 Types of Square Roots Reals Perfect Squares Irrationals Rationals 1 1 4 9 16 25 36 49 64 81 100 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

3 Types of Square Roots Reals Imaginary Irrationals Rationals The square root of any negative number will be an imaginary number. Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 1) 0 Whole, Integer, Rational, Real 2) - 2.03 Rational, Real 3) Irrational, Real 4) Integer, Rational, Real Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Identify all of the sets to which each number belongs. (Reals, Rationals, Irrationals, Integers, Wholes, Naturals) 5) None ( Imaginary ) 6) Integer, Rational, Real 7) Irrational, Real 8) None ( Imaginary ) Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Domain- the set of values which may be meaningfully substituted for a given variable. Which set of numbers would best describe the variable? 1) Let x = the number of people at a meeting. D: x Naturals “ is a member of ” 2) Let y = your weight D: y Positive Reals 3) Let t = the low temperature in Alaska yesterday D: t Reals 4) Let n = the low recorded temperature in Alaska. D: n Integers Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Graph t < 3 over the given domain. 1) D: Reals -3 -2 -1 0 1 2 3 4 2) D: Integers -3 -2 -1 0 1 2 3 4 3) D: Wholes -3 -2 -1 0 1 2 3 4 Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series

Let A = Natural numbers less than 4 Let B = Integers between -3 and 2 Let C = Real numbers greater than -1 List the elements of the following given the sets above. 1) A 4) { 1, 2, 3 } { -2, -1, 0, 1, 2, 3 } 2) B 5) { -2, -1, 0, 1 } { 0, 1 } 3) 6) { 1 } { 1, 2, 3 } Algebra I by James Wenk © 2003 published by TEACHINGpoint as part of the Expert Systems for Teachers Series