Section 2.1
The Real Number Line
Number Review
• Natural or Counting Numbers: ____________________________
Ex: ___________________________________
• Whole Numbers: ____________________________
• Integers: ____________________________
Ex: ___________________________________
• Rational Numbers: _________________________________________
Ex: ___________________________________
• Irrational Numbers: Numbers that cannot be expressed as a quotient of
two integers.
Examples:__________________________
• Real Numbers: All _______________ and _______________ numbers.
Graphing Real Numbers
A real number line is a horizontal line used to picture real numbers.
Real Number Line
• The scale marks are equally spaced and represent ______________.
• The ___________ is the point labeled 0 is________________________.
• _______________ numbers are represented as points to the left of zero.
• ______________ numbers are represented as points to the right of zero.
• _____________________ are represented by points on the number line.
• ______________________________________ is drawing the point that
corresponds to a real number.
Example: Draw points on a real number line.
5
Graph the numbers 1.7, -3.6, and .
2
-5
-4 -3
-2
-1
0
1
2
3
4
5
The point that corresponds to 1.7 is 1.7 units ________ of the origin or 0.
The point that corresponds to -3.6 is 3.6 units to the ________ of 0.
The point that corresponds to
5
is 2.5 units to the ________ of the origin.
2
Comparing real numbers on the real number line.
Write inequalities to compare the numbers on the above number line.
a. -3.6 and 1.7
________
b.
5
and 1.7
2
________
c. 1.7 and 0
________
Ordering real numbers.
1
Write the following numbers in increasing order. -1.5, , -3, 2.5, 0, -1
3
Use the number line to graph the numbers.
-5
-4 -3
-2
-1
0
1
2
3
From the graph you can see the order is -3, -1.5, -1, 0,
4
5
1
, and 2.5.
3
Finding Opposites and Absolute Values.
_____________ are two points that are the same distance from the origin,
but on opposite sides of the origin.
-3
3
•
•
-5 -4 -3 -2 -1
0 1 2 3 4 5
• __________________________________________________________
• The expression -3 is read as either ___________ or the _____________.
• You read -a as the ________________.
You should not assume that -a is a negative number.
Example: _________________________________
The ___________________ of a real number is the distance between the
origin and the point representing the real number.
The symbol_____ represents the absolute value of a number a.
• If a is a positive number, then________.
Example: ________
• If a is zero, then ________.
Example:
________
• If a is a negative number, then ________.
Example:
________
Examples: Evaluate the expressions.
a. 3.7
b. −2.6
c.
9
8
d.
−7
3
e. 0
Example: Finding Velocity and Speed.
An object is dropped close to the Earth’s surface. The rate at which it is
falling 1 second later is 32 ft/sec. What is the object’s velocity and speed
1 second after it is dropped.
Hint: Velocity indicates both speed and direction. Up is___________ and
down is ___________. Speed is the ________________ of velocity.
Solution:
Velocity = ___________
Speed =___________
Example: Solve the Absolute Value equation mentally.
1) x = 6
___________
2) x = −5
___________
3) x = −2
___________
4) − x = 1
___________