This document discusses different types of real numbers and how they can be represented on a number line. It defines whole numbers, integers, rational numbers, irrational numbers, and real numbers. Rational numbers can be represented as terminating or repeating decimals. Irrational numbers are non-terminating and non-repeating. A number line pairs each real number with a point, and the distance between two points is the absolute value of the difference of their coordinates.

1. Real Numbers and Number LinesReal Numbers and Number Lines
You will learn to find the distance between two points on a
number 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 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 _____________ .

3. 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

4. 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.

5. 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 _________.

6. 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

7. Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ .

8. 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

9. 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

10. 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.

11. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−

12. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−

13. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b

14. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction

15. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero

16. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
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.

17. Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
−
5
3
− 11
8
−
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
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.infinitely

18. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.

19. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=

20. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.

21. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating
0.375
0.49
terminating decimals.

22. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.

23. Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.
The three periods following the digits in the nonterminating decimals indicate
that there are infinitely many digits in the decimal.
The three periods following the digits in the nonterminating decimals indicate
that there are infinitely many digits in the decimal.

24. 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.

25. 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=

26. 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.

27. Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.

28. Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers

29. Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers
6.028716 . . .
and
0.101001000 . . .
appear to be irrational numbers

30. Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.
0 21-1-2 3
81.8603 . . .− 0.8− 0.6 1.762 . . .0.25−

31. Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 3
81.8603 . . .− 0.8− 0.6 1.762 . . .0.25−

32. 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 3
81.8603 . . .− 0.8− 0.6 1.762 . . .0.25−

33. 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 2-1
Number Line
Postulate
Each real number corresponds to exactly one point on a number
line.
Each point on a number line corresponds to exactly one real
number
0 21-1-2 3
81.8603 . . .− 0.8− 0.6 1.762 . . .0.25−

34. 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.

35. 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

36. 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

37. 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

38. 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

39. 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

40. 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

41. 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

42. Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using 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 distance
between the points.

43. Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using 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 distance
between the points.
AB
measure

44. Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using 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 distance
between the points.
AB
measure
Postulate 2-3
Ruler
Postulate
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.

45. Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using 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 distance
between the points.
AB
measure
Postulate 2-3
Ruler
Postulate
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.
measure = a – b
B A
ab

46. 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 difference
10 – 2, or 8.
Another way to calculate the measure of the distance is by using
____________.

47. 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 difference
10 – 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 1

48. 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 =

49. 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 =
5 8
3 3
 
− − − ÷
 
3
3
=
1=
CF =

50. 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 =
5 8
3 3
 
− − − ÷
 
3
3
=
1=
CF = ( 1) 2− −
3= −
3=

51. 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 =

52. 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 =
1 8
3 3
 
− − − ÷
 
7
3
=
7
3
=
EF =

53. Real Numbers and Number LinesReal Numbers and Number Lines