Transcript Lesson 2-1 Real Numbers and Number Lines

Lesson 2-1
Real Numbers and Number
Lines
Ohio Content Standards:
Ohio Content Standards:
• Apply properties of operations and the
real number system, and justify when
they hold for a set of numbers.
Whole Numbers
Whole Numbers
• Includes zero and the Natural Numbers
Whole Numbers
• Includes zero and the Natural Numbers
• Natural Numbers are also called the
Counting Numbers
Integers
Integers
• Includes zero, the positive integers, and
the negative integers
Rational Numbers
Rational Numbers
• Any number that can be written as a
fraction
Rational Numbers
• Any number that can be written as a
fraction
• Terminating Decimals are rational
Rational Numbers
• Any number that can be written as a
fraction
• Terminating Decimals are rational
• Repeating Decimals are rational
Irrational Numbers
Irrational Numbers
• Decimals that are nonterminating and do
not repeat
Real Numbers
Real Numbers
• Include both rational and irrational
numbers
Postulate 2-1
Number Line Postulate
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.
For each situation, write a real number
with ten digits to the right of the
decimal point.
For each situation, write a real number
with ten digits to the right of the
decimal point.
• A rational number between 6 and 8 with
a 2-digit repeating pattern
For each situation, write a real number
with ten digits to the right of the
decimal point.
• A rational number between 6 and 8 with
a 2-digit repeating pattern
• An irrational number greater than 5
Coordinate
Coordinate
• Number that corresponds to a point on a
number line
Origin
Origin
• Has coordinate zero
Postulate 2-2
Distance Postulate
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.
Postulate 2-3
Ruler Postulate
Postulate 2-3
Ruler Postulate
• Points on a line are paired with the real
numbers, and the measure of the
distance between two points is the
positive difference of the corresponding
numbers.
Absolute Value
Absolute Value
• Number of units a number is from zero
on the number line.
Absolute Value
• Number of units a number is from zero
on the number line.
• Symbol : two vertical slashes
Use the number line to find CE.
A
-3
B
-2
C
-1
D
E
0
F
1
2
G
3
Erin traveled on I-85 from Durham,
North Carolina, to Charlotte. The
Durham entrance to I-85 that she
used is at the 173-mile marker, and
the Charlotte exit she used is at the
39-mile marker. How far did Erin
travel on I-85?
Assignment:
Pgs. 54 - 55
12-28 evens,
32-36 evens