Transcript 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” “Doesn’t Make Sense”
Rational Numbers
-Any number that can be written as a fraction.
fractions wholes integers decimals terminating 2 3 7 18 7 1 18 1 0.49
49 100 repeating decimals 0.7
7 9 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 2 3 Rationals , 7, -0
.
4 - any number that can be written as a fraction.
Irrationals 2 - non-terminating and non-repeating decimals Fractions/Decimals 1 6 4 , -0
.
32, - 2
.
1 Integers
…
-3, -2, -1, 0, 1, 2, 3
...
Negative Integers
…
-3, -2, -1 Zero 0 Wholes 0, 1, 2, 3
...
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
2 3 -3 Rationals Integers -19 -2
.
65 Wholes 0 6 1 4 Naturals 1, 2, 3
...
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) 6 Irrational , Real 5) 8 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 9) 25 Natural ,Whole, Integer, Rational , Real Integer, Rational , Real 10) 8 Irrational , Real
Graph on Number Line
• (Hint: turn them all into decimals) 2 , 3 1 , 5 8, 10 3
0.6, 0.2, 2.9, 3.3
-1 0 1 2 3 4 5 6
Order From Least to Greatest
8 8, 4, 5 2 , 3.75
5 2 -4 -3 -2 -1 0 1 2 3 4, 3.75, 5 2 , 4 5 6 8 7
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 2 3 0.6
0.6
0.6
5 8
<
0.625
0.65
5 9
>
5 9 5 10 4) 3 10 1 3
Homework
Page 455 (12-46) even • Write the title • Write the number and question • Show work • Highlight answer