1. 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

2. 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

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

4. 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

5. …-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

6. 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

7. 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

8. 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

9. 3 Types of Square Roots Reals Perfect Squares Irrationals Rationals 11 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

10. 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

11. Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) 0
Whole, Integer, Rational, Real 2)
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

12. 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

13. 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

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

15. 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