vijender x
TRANSCRIPT
Real Numbers and Number LinesReal Numbers and Number Lines
You will learn to find the distance between two points on anumber line.
1) Whole Numbers2) Natural Numbers3) Integers4) Rational Numbers5) Terminating Decimals6) Nonterminating Decimals7) Irrational Numbers8) Real Numbers9) Coordinate10 Origin11) Measure12) Absolute Value
Real Numbers and Number LinesReal 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.
0 21 43 65 7 98 10
This figure shows the set of _____________ .
Real Numbers and Number LinesReal 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.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
Real Numbers and Number LinesReal 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.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
Real Numbers and Number LinesReal 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.
0 21 43 65 7 98 10
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 _________.
Real Numbers and Number LinesReal 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.
0 21 43 65 7 98 10
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 _________.indefinitely
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ .
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integers
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
The integers include zero, the positive integers, and the negative integers.The arrows indicate that the numbers go on forever in both directions.
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.
0 21-1-2 43
38
23
138
15
53
118
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
A rational number is any number that can be written as a _______,where a and b are integers and b cannot equal ____.
ab
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
A rational number is any number that can be written as a _______,where a and b are integers and b cannot equal ____.
ab
fraction
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
A rational number is any number that can be written as a _______,where a and b are integers and b cannot equal ____.
ab
fractionzero
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
A rational number is any number that can be written as a _______,where a and b are integers and b cannot equal ____.
ab
fractionzero
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.
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 43
38
23
138
15
53
118
A rational number is any number that can be written as a _______,where a and b are integers and b cannot equal ____.
ab
fractionzero
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.infinitely
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3 0.3758
2 0.666 . . .3
0 07
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3 0.3758
2 0.666 . . .3
0 07
Decimals may be __________ or _____________.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3 0.3758
2 0.666 . . .3
0 07
Decimals may be __________ or _____________.terminating
0.3750.49 terminating decimals.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3 0.3758
2 0.666 . . .3
0 07
Decimals may be __________ or _____________.terminating nonterminating
0.3750.49 terminating decimals.
0.666 . . .-0.12345 . . . nonterminating decimals.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3 0.3758
2 0.666 . . .3
0 07
Decimals may be __________ or _____________.terminating nonterminating
0.3750.49 terminating decimals.
0.666 . . .-0.12345 . . . nonterminating decimals.
The three periods following the digits in the nonterminating decimals indicatethat there are infinitely many digits in the decimal.
Real Numbers and Number LinesReal 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.
Real Numbers and Number LinesReal 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.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17
Real Numbers and Number LinesReal 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.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17
Each rational number can be expressed as a terminating decimal or a nonterminating decimal with a repeating pattern.
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat are called _______________.
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat are called _______________.irrational numbers
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat are called _______________.irrational numbers
6.028716 . . . and0.101001000 . . .
appear to be irrational numbers
Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.
0 21-1-2 381.8603 . . . 0.8 0.6 1.762 . . .0.25
Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 381.8603 . . . 0.8 0.6 1.762 . . .0.25
Real Numbers and Number LinesReal Numbers and Number Lines
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 381.8603 . . . 0.8 0.6 1.762 . . .0.25
Real Numbers and Number LinesReal Numbers and Number Lines
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
Postulate 2-1Number Line
Postulate
Each real number corresponds to exactly one point on a numberline. Each point on a number line corresponds to exactly one realnumber
0 21-1-2 381.8603 . . . 0.8 0.6 1.762 . . .0.25
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the_________ of the point.
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the_________ of the point.coordinate
Real Numbers and Number LinesReal 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.
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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.
The coordinate of point B is __
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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.
The coordinate of point B is __-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
origin
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal 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 2-2DistancePostulate
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.
Real Numbers and Number LinesReal 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 2-2DistancePostulate
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.
AB
measure
Real Numbers and Number LinesReal 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 2-2DistancePostulate
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.
AB
measure
Postulate 2-3Ruler
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.
Real Numbers and Number LinesReal 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 2-2DistancePostulate
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.
AB
measure
Postulate 2-3Ruler
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.
measure = a – b
B A
ab
Real Numbers and Number LinesReal Numbers and Number Lines
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference10 – 2, or 8.
Another way to calculate the measure of the distance is by using____________.
Real Numbers and Number LinesReal Numbers and Number Lines
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference10 – 2, or 8.
Another way to calculate the measure of the distance is by using____________.absolute value
10 2AB
8
8
2 10BA
8
8
1 2 43 5 76 8 9 10 11
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA CF
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA5 83 3
33
1
CF
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA5 83 3
33
1
CF ( 1) 2
3
3
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA EF
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA1 83 3
73
73
EF
Real Numbers and Number LinesReal Numbers and Number Lines