September 14, 2015
3.1 Rational Numbers
REAL NUMBERS
Rational Numbers (Q)
Integers (Z)
Whole Numbers (W)
Natural Numbers (N)
Irrational Numbers
September 14, 2015
Rational Number:
any number that can be written as a ratio
of integers (aka a fraction)
examples: 2, ½, -¾, 0.5, 0.33
Irrational Number:
any number that cannot be written as a
ratio of integers (aka cannot be written as
a fraction)
examples: √3, π, √5
Real Number:
any number: rational and irrational
September 14, 2015
Review:
Fractions to decimals ...
7/25
3/8
7/10
September 14, 2015
Review:
Fractions to decimals ...
1/6
4/9
5/12
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September 14, 2015
All rational numbers (aka. fractions) can be
written as decimals.
examples: 0.5, 0.33
... decimals that
end or repeat.
Irrational numbers cannot be written as a
fractions, which means that they are
decimals that do NOT end and do NOT
repeat.
examples: √3, π, √5
TERMINATING AND
REPEATING DECIMALS
A decimal that ends or terminates.
EXAMPLE: 0.5 0.814 1.03
REPEATING DECIMAL
Pull
TERMINATING
DECIMAL
Pull
a
digits
__
1212
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Converting a Decimal to a
Fraction.
.35
.325
35
35
5
100
100
5
7
20
325
1000
325
1000
25
13
25
40
September 14, 2015
Review:
Decimals to fractions ...
0.23
2.007
0.925
-0.48
September 14, 2015
September 14, 2015
Converting a Repeating Decimal to Fraction
1/9 =
1/99 =
1/999 =
2/9 =
2/99 =
2/999 =
3/9 =
3/99 =
4/9 =
4/99 =
43/999 =
5/9 =
6/9 =
15/99 =
115/999 =
7/9 =
8/9 =
37/999 =
23/99 =
230/999 =
67/99 =
627/999 =