Objective TSW identify the parts of the Real Number System TSW define rational and irrational numbers TSW classify numbers as rational or irrational Real Numbers Real Numbers are every number Therefore any number that you can find on the number line ID: 696047
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Slide1
REAL NUMBERS
(as opposed to fake numbers?)Slide2
Objective
TSW identify the parts of the Real Number SystemTSW define rational and irrational numbersTSW classify numbers as rational or irrationalSlide3
Real Numbers
Real Numbers are every number.Therefore, any number that you can find on the number line.
Real Numbers have two categories.Slide4
What does it Mean?
The number line goes on forever.Every point on the line is a REAL number.
There are no gaps on the number line.
Between the whole numbers and the fractions there are numbers that are decimals but they don’t terminate and are not recurring decimals. They go on forever.Slide5
Real Numbers
REAL NUMBERS
-8
-5,632.1010101256849765…
61
49%
π
549.23789
154,769,852,354
1.333Slide6
Two Kinds of Real Numbers
Rational Numbers
Irrational NumbersSlide7
Rational Numbers
A rational number is a real number that can be written as a fraction.
A rational number written in decimal form is terminating or repeating.Slide8
Examples of Rational Numbers
161/2
3.56
-8
1.3333…
- 3/4Slide9
Integers
One of the subsets of rational numbersSlide10
What are integers?
Integers are the whole numbers and their opposites.Examples of integers are
6
-12
0
186
-934Slide11
Integers are rational numbers because they can be written as fraction with 1 as the denominator.Slide12
Types of Integers
Natural Numbers(N):
Natural Numbers are counting numbers from 1,2,3,4,5,................
N
= {1,2,3,4,5,................}
Whole Numbers (W):
Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............
W
= {0,1,2,3,4,5,..............}
W = 0 + NSlide13
WHOLE
Numbers
REAL NUMBERS
IRRATIONAL
Numbers
NATURAL
Numbers
RATIONAL
Numbers
INTEGERSSlide14
Irrational Numbers
An irrational number is a number that cannot
be written as a fraction of two integers.
Irrational numbers written as decimals are non-terminating and non-repeating.Slide15
A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Caution!
Irrational numbers
can be written only as decimals that do
not
terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. Slide16
Examples of Irrational Numbers
Pi
Slide17
Try this!
a) Irrational
b) Irrational
c) Rational
d) Rational
e) IrrationalSlide18
Additional Example 1: C
lassifying Real Numbers
Write all classifications that apply to each number.
5 is a whole number that is not a perfect square.
5
irrational, real
–12.75 is a terminating decimal.
–12.75
rational, real
16 2
whole, integer, rational, real
= = 2
4 2
16 2
A.
B.
C.Slide19
A fraction with a denominator of 0 is undefined because you cannot divide by zero. So it is not a number at all.Slide20
State if each number is rational, irrational, or not a real number.
21
irrational
0 3
rational
0 3
= 0
Additional Example 2: D
etermining the Classification of All Numbers
A.
B.Slide21
not a real number
Additional Example 2: D
etermining the Classification of All Numbers
4
0
C.
State if each number is rational, irrational, or not a real number.Slide22
Objective
TSW compare rational and irrational numbersTSW order rational and irrational numbers on a number lineSlide23
Comparing Rational and Irrational Numbers
When comparing different forms of rational and irrational numbers, convert the numbers to the same form.
Compare -3 and -3.571
(convert -3 to -3.428571…
-3.428571… > -3.571
3
7
3
7Slide24
Practice
Slide25
Ordering Rational and Irrational Numbers
To order rational and irrational numbers, convert all of the numbers to the same form.You can also find the approximate locations of rational and irrational numbers on a number line.Slide26
Example
Order these numbers from least to greatest.
¹/
₄
, 75%, .04, 10%,
⁹/₇
¹/₄ becomes 0.25
75% becomes 0.75
0.04 stays 0.04
10% becomes 0.10
⁹/₇ becomes 1.2857142…
Answer:
0.04, 10%,
¹/
₄, 75%, ⁹/₇ Slide27
Practice
Order these from least to greatest: