Real Numbers and Number Lines

1
Real Numbers and Number Lines
What You'll Learn
You will learn to find the distance between two
points on anumber line.
1) Whole Numbers 2) Natural Numbers 3)
Integers 4) Rational Numbers 5) Terminating
Decimals 6) Nonterminating Decimals 7) Irrational
Numbers 8) Real Numbers 9) Coordinate 10
Origin 11) Measure 12) Absolute Value
2
Real Numbers and Number Lines
Numbers that share common properties can be
classified or grouped into sets. Different sets
of numbers can be shown on numbers lines.
This figure shows the set of _____________ .
3
Real Numbers and Number Lines
Numbers that share common properties can be
classified or grouped into sets. Different sets
of numbers can be shown on numbers lines.
This figure shows the set of _____________ .
whole numbers
4
Real Numbers and Number Lines
Numbers that share common properties can be
classified or grouped into sets. Different sets
of numbers can be shown on numbers lines.
This figure shows the set of _____________ .
whole numbers
The whole numbers include 0 and the natural, or
counting numbers.
5
Real Numbers and Number Lines
Numbers that share common properties can be
classified or grouped into sets. Different sets
of numbers can be shown on numbers lines.
This figure shows the set of _____________ .
whole numbers
The whole numbers include 0 and the natural, or
counting numbers.
The arrow to the right indicate that the whole
numbers continue _________.
6
Real Numbers and Number Lines
Numbers that share common properties can be
classified or grouped into sets. Different sets
of numbers can be shown on numbers lines.
This figure shows the set of _____________ .
whole numbers
The whole numbers include 0 and the natural, or
counting numbers.
indefinitely
The arrow to the right indicate that the whole
numbers continue _________.
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Real Numbers and Number Lines
This figure shows the set of _______ .
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Real Numbers and Number Lines
This figure shows the set of _______ .
integers
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Real Numbers and Number Lines
This figure shows the set of _______ .
integers
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Real Numbers and Number Lines
This figure shows the set of _______ .
integers
The integers include zero, the positive integers,
and the negative integers.The arrows indicate
that the numbers go on forever in both directions.
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Real Numbers and Number Lines
A number line can also show ______________.
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
fraction
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
fraction
zero
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
fraction
zero
The number line above shows some of the rational
numbers between -2 and 2.
In fact, there are _______ many rational numbers
between any two integers.
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Real Numbers and Number Lines
A number line can also show ______________.
rational numbers
fraction
zero
The number line above shows some of the rational
numbers between -2 and 2.
infinitely
In fact, there are _______ many rational numbers
between any two integers.
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
decimals
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
decimals
Decimals may be __________ or _____________.
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
decimals
terminating
Decimals may be __________ or _____________.
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
decimals
terminating
nonterminating
Decimals may be __________ or _____________.
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Real Numbers and Number Lines
Rational numbers can also be represented by
________.
decimals
terminating
nonterminating
Decimals may be __________ or _____________.
The three periods following the digits in the
nonterminating decimals indicatethat there are
infinitely many digits in the decimal.
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Real Numbers and Number Lines
Some nonterminating decimals have a repeating
pattern.
0.17171717 . . . repeats the digits 1 and 7
to the right of the decimal point.
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Real Numbers and Number Lines
Some nonterminating decimals have a repeating
pattern.
0.17171717 . . . repeats the digits 1 and 7
to the right of the decimal point.
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Real Numbers and Number Lines
Some nonterminating decimals have a repeating
pattern.
0.17171717 . . . repeats the digits 1 and 7
to the right of the decimal point.
Each rational number can be expressed as a
terminating decimal or a nonterminating decimal
with a repeating pattern.
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Real Numbers and Number Lines
Decimals that are nonterminating and do not
repeat are called _______________.
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Real Numbers and Number Lines
Decimals that are nonterminating and do not
repeat are called _______________.
irrational numbers
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Real Numbers and Number Lines
Decimals that are nonterminating and do not
repeat are called _______________.
irrational numbers
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Real Numbers and Number Lines
____________ include both rational and irrational
numbers.
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Real Numbers and Number Lines
Real numbers
____________ include both rational and irrational
numbers.
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Real Numbers and Number Lines
Real numbers
____________ include both rational and irrational
numbers.
The number line above shows some real numbers
between -2 and 2.
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Real Numbers and Number Lines
Real numbers
____________ include both rational and irrational
numbers.
The number line above shows some real numbers
between -2 and 2.
Postulate 2-1 Number Line Postulate Each real number corresponds to exactly one point on a numberline. Each point on a number line corresponds to exactly one realnumber
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
35
Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
A
C
B
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
10
A
C
B
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
10
The coordinate of point B is __
A
C
B
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
10
The coordinate of point B is __
-4
A
C
B
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
10
The coordinate of point B is __
-4
Point C has coordinate 0 and is called the _____.
A
C
B
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Real Numbers and Number Lines
The number that corresponds to a point on a
number line is called the_________ of the point.
coordinate
On the number line below, __ is the coordinate of
point A.
10
The coordinate of point B is __
-4
origin
Point C has coordinate 0 and is called the _____.
A
C
B
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Real Numbers and Number Lines
The distance between two points A and B on a
number line is found byusing the Distance and
Ruler Postulates.
Postulate 2-2 Distance Postulate For any two points on a line and a given unit of measure, there is a unique positive real number called the measure of the distancebetween the points.
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Real Numbers and Number Lines
The distance between two points A and B on a
number line is found byusing the Distance and
Ruler Postulates.
Postulate 2-2 Distance Postulate For any two points on a line and a given unit of measure, there is a unique positive real number called the measure of the distancebetween the points.
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Real Numbers and Number Lines
The distance between two points A and B on a
number line is found byusing the Distance and
Ruler Postulates.
Postulate 2-2 Distance Postulate For any two points on a line and a given unit of measure, there is a unique positive real number called the measure of the distancebetween the points.
Postulate 2-3 Ruler Postulate Points on a line are paired with real numbers, and the measure ofthe distance between two points is the positive difference of the corresponding numbers.
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Real Numbers and Number Lines
The distance between two points A and B on a
number line is found byusing the Distance and
Ruler Postulates.
Postulate 2-2 Distance Postulate For any two points on a line and a given unit of measure, there is a unique positive real number called the measure of the distancebetween the points.
Postulate 2-3 Ruler Postulate Points on a line are paired with real numbers, and the measure ofthe distance between two points is the positive difference of the corresponding numbers.
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Real Numbers and Number Lines
The measure of the distance between B and A is
the positive difference10 2, or 8.
A
B
Another way to calculate the measure of the
distance is by using____________.
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Real Numbers and Number Lines
The measure of the distance between B and A is
the positive difference10 2, or 8.
A
B
Another way to calculate the measure of the
distance is by using____________.
absolute value
48
Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Use the number line below to find the following
measures.
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Real Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile
marker 313.The Hays exit is mile marker 154.
What is the distance between these two towns?
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Real Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile
marker 313.The Hays exit is mile marker 154.
What is the distance between these two towns?
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Real Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile
marker 313.The Hays exit is mile marker 154.
What is the distance between these two towns?
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Real Numbers and Number Lines
End of Lesson