Download 9_2 The real number system

Lesson 9.2
The Real Number System
Objective - To classify and identify
numbers within the real number
system.
Understanding Rational and Irrational
“Makes Sense”
Rational Numbers
-Any number that can
be written as a fraction.
2
3
7
wholes
71

18
integers 18 
1
terminating
49
0.49 
decimals
100
repeating
7
decimals 0.7  9
fractions
“Doesn’t Make Sense”
Irrational Numbers
-Non-terminating and
non-repeating decimals.
-can’t be written as a
fraction.
3  1.73205...
1.212112111211112...
0.123456789101112...
0.15255355545555...
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 and irrationals.
Sets of Numbers
Reals
Rationals - any number that
can be written as a
2
, 7, -0 4 fraction.
3
Irrationals - non-terminating
.
Fractions/Decimals
1
6 , -0 32, - 2 1
4
.
.
2
and
non-repeating
decimals
Integers
…-3, -2, -1, 0, 1, 2, 3...
Negative Integers
Wholes
…-3, -2, -1
0, 1, 2, 3...
Zero
0
Naturals
1, 2, 3...
Sets of Numbers
This is a Venn Diagram that displays the following sets of numbers:
Naturals, Wholes, Integers, Rationals, Irrationals, and Reals.
Reals
Rationals
2
3
-2.65
Integers
-3
-19
Wholes
0
Naturals
1, 2, 3...
1
6
4
Irrationals
2
Identify each number below as natural, whole,
integer, rational, irrational, or real. More than one
may apply.
1) 7
8
Rational , Real
2) 0
Whole , Integer , Rational, Real
3)  24
Integer , Rational , Real
4)
Irrational , Real
5) 8
6
Natural ,Whole , Integer , Rational , Real
Identify each number below as natural, whole,
integer, rational, irrational, or real. More than one
may apply.
6)  4
5
Rational , Real
7)  9
Integer , Rational, Real
8) 16
Natural ,Whole , Integer , Rational , Real
9)  25
10) 8
Integer , Rational, Real
Irrational , Real
Graph on Number Line
• (Hint: turn them all into decimals)
2 1
, ,
3 5
10
8,
3
0.6, 0.2, 2.9, 3.3
-1
0
1
2
3
4
5
6
Order From Least to Greatest
5
8, 4, , 3.75
2
5
8  2.9, 4,  2.5, 3.75
2
-4 -3 -2 -1 0
1 2 3
4 5 6 7
5
4, 3.75,
,
2
8
Compare Using < > or =
• Turn them both either to:
– Fractions and use the heart method
– Decimals and compare place values
Use <, >, or = to compare.
1)
4
9
= 0.6
2
 0.6
3
3) 5
9
> 0.5
5
5

9
10
0.6  0.6
2) 5
8
< 0.65
0.625  0.65
4) 3 <
10
1
3
Homework
•
•
•
•
Page 455 (12-46) even
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