Download Take out a calculator!!!

Take out a calculator!!!
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Natural Numbers - Natural counting numbers.
1, 2, 3, 4 …
Whole Numbers - Natural counting numbers and zero.
0, 1, 2, 3 …
Integers - Whole numbers and their opposites.
… -3, -2, -1, 0, 1, 2, 3 …
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1
Rational Numbers - Integers, fractions, and decimals.
2
2
, -0.8 , 2.39 , 14 , -3
Ex:
3
5
Irrational Numbers - Any decimal number which
can’t be written as a fraction. A non-terminating and
non-repeating decimal.
8
2
11
Reals - Rational & Irrational Numbers
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Rationals
- any number which
2
can be written as a
, 7, -0.4 fraction.
3
Irrationals
- non-terminating
and non-repeating
decimals
π
Fractions/Decimals
6
1 , -0.32, - 2.1
4
≈ 3141592
.
...
2
Integers
…-3, -2, -1, 0, 1, 2, 3...
Negative Integers
Wholes
0, 1, 2, 3...
…-3, -2, -1
Zero
0
Naturals
1, 2, 3...
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2
A Venn Diagram can show our number system:
Reals, Rationals, Irrationals, Integers, Wholes,
and Naturals.
Reals
Rationals
2
3
Integers
-3
Wholes
-2.65
-19
0
6
Naturals
1
4
1, 2, 3...
Irrationals
π
2
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Imaginary Numbers
−2
Reals
Rationals
2
3
Integers
-3
Wholes
-2.65
-19
0
6
Naturals
1, 2, 3...
1
4
Irrationals
π
2
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3
Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
Integer, Rational, Real
1) -6
2) −5
7
Rational, Real
8
3) 14 Natural, Whole, Integer, Rational, Real
4) 6π Irrational, Real
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Identify all of the sets to which each number belongs.
(Reals, Rationals, Irrationals, Integers, Wholes, Naturals)
1) 0
Whole, Integer, Rational, Real
2) - 2.03 Rational, Real
3) 2 3
Irrational, Real
4) −10 Integer, Rational, Real
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4
Identify each root as rational or irrational.
1) 10 irrational
2)
6)
25 rational
62 irrational
7) 81 rational
3) 15 irrational
8) − 16
4) − 49 rational
9)
5)
50 irrational
99
rational
irrational
10) 121 rational
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-5 -4 -3 -2 -1 0 1 2 3 4 5
π
6
3
Graph the rational numbers on a number line.
−3 −1 1 −0.4
2
−3
−1
1
2
6
3
−0.4
π
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5
-5 -4 -3 -2 -1 0 1 2 3 4 5
−5.2
3
1.5 24 4 1
2
8
2
Graph the rational numbers on a number line.
−5.2
−
4
1
2
−
3
2
1.5
24
8
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When comparing rational numbers you must
find a common denominator!
28
=
35
( 77ii ) 54
>
( )
5 i5 = 25
7 i5
35
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6
When comparing rational numbers you must
find a common denominator!
( )
−10 2i −5
= 2i 8
16
<
()
−9 i1 = −9
16 i1
16
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When comparing rational numbers you must
find a common denominator!
( )
15 3i 5
=
36 3i 12
<
( )
4 i4
16
=
9 i4
36
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7
When comparing rational numbers you must
find a common denominator!
1)
4
9
2) 7
3
= 0.6
>
5
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Aren’t rational numbers
interesting?
Take out your
study guide
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8
#4
Rational vs. Irrational
RATIONAL NUMBERS
CAN BE WRITTEN AS:
IRRATIONAL NUMBERS
CANNOT BE WRITTEN AS:
•The quotient of two
integers (a fraction)
•Terminating decimal
•Repeating decimal
•A fraction
•A decimal that terminates or
repeats.
•Because they go on forever…
Some square roots are irrational
Perfect square roots are
rational
1
4
2
3
5
9
16
6
7
8
MAKE SENSE!
DOESN’T MAKE SENSE
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#5
This Venn Diagram shows Reals, Rationals, Irrationals,
Integers, Wholes, and Naturals.
Reals
Rationals
2
3
Integers
-3
Wholes
-15
0
Naturals
-2.5
6
1
4
1, 2, 3...
Irrationals
π
2
copyright©amberpasillas2010
9
#6
IRRATIONAL
RATIONAL
Any number which can
be written as a fraction
Ex:
7 =
7
1
2.08 = 2
0. 3 =
Non-terminating and nonrepeating decimals which
can’t be written as fractions.
π ≈ 3.14159...
Ex:
.
...
2 ≈ 1414213
8
100
1
3
1
=
−
5
−5.1
9
1.23456789...
8 ≈ 2.828427...
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10