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Lesson 9.2The Real Number SystemObjective - To classify and identify numbers within the real number system.
Understanding Rational and Irrational
Rational Numbers Irrational Numbers-Any number that can be written as a fraction.
-Non-terminating and non-repeating decimals.
“Makes Sense” “Doesn’t Make Sense”
-can’t be written as a fraction.
237
18
0.49
0.7
fractions
wholes
integers
terminatingdecimalsrepeatingdecimals
71
181
49100
79
3 1.73205...1.212112111211112...
0.123456789101112...
0.15255355545555...
Sets of NumbersNaturals - 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 and irrationals.
Sets of NumbersReals
Rationals Irrationals- any number thatcan be written as afraction.
2
3, 7, -0.4
Fractions/Decimals Integers
61
4 , -0.32, - 2.1 …-3, -2, -1, 0, 1, 2, 3...
Negative Integers Wholes…-3, -2, -1 0, 1, 2, 3...
Zero0
Naturals1, 2, 3...
- non-terminating and non-repeating decimals
2
This is a Venn Diagram that displays the following sets of numbers: Naturals, Wholes, Integers, Rationals, Irrationals, and Reals.
Naturals1, 2, 3...
Wholes0
Integers-3 -19
Rationals2
3
61
4
-2.65
Irrationals
2
Reals
Sets of Numbers
Identify each number below as natural, whole,integer, rational, irrational, or real. More than onemay apply.
71) 8
2) 0
3) 24
4) 6
5) 8
Rational , Real
Whole, Integer, Rational , Real
Integer, Rational , Real
Irrational , Real
,Whole, Integer, Rational , RealNatural
Identify each number below as natural, whole,integer, rational, irrational, or real. More than onemay apply.
46) 5
7) 9
8) 16
9) 25
10) 8
Rational , Real
Integer, Rational , Real
,Whole, Integer, Rational , RealNatural
Integer, Rational , Real
Irrational , Real
Graph on Number Line
• (Hint: turn them all into decimals)
2 1 10, , 8,
3 5 3
0.6,0.2,2.9,3.3
-1 0 1 2 3 4 5 6
Order From Least to Greatest
58, 4, , 3.75
2
58 2.9, 4, 2.5, 3.75
2
-4 -3 -2 -1 0 1 2 3 4 5 6 75
4, 3.75, , 82
Compare Using < > or =
• Turn them both either to:– Fractions and use the heart method – Decimals and compare place values
Use <, >, or = to compare.
41) 0.69
52) 0.658
53) 0.59
3 14) 10 3
=
<
>
<
20.6
3
0.6 0.6
0.625 0.65
5 5
9 10
Homework
Page 455 (12-46) even
• Write the title
• Write the number and question
• Show work
• Highlight answer