1-8 Number Systems

1
1-8 Number Systems
Square Roots
Add closure property?
You will be allowed to use a calculator for
tomorrows lesson but NOT on the CHAPTER 1 test!
NO GRAPHING CALCULATORS!
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
REAL NUMBERS
Rational Numbers Any number that can be written
in the form of . As a decimal they repeat or
terminate. ex Repeats ex
Terminates
Irrational Numbers ex ? and These
must be represented by a symbol (ex ?), or as a
rounded number, or in radical form because the
decimal doesnt repeat or terminate (stop).
Integers Whole numbers and their opposites
(this means positive and negative whole numbers).
ex ? 4, 3, 2, 1, 0, 1 ?, 2 ?, 3 ?, 4
Whole Numbers Natural Numbers and zero. ex
0,1,2,3
Natural or Counting Numbers ex 1,2,3,4,
3
You will need a calculator for todays lesson.
While you are allowed to use a calculator for
todays lesson, you will NOT be allowed to use
one on the CHAPTER 1 test! NO GRAPHING
CALCULATORS!
4
You must learn how to use a calculator! There
are many makes and models. Read the instruction
booklet.
Enter a problem into the calculator for which you
already know the answer. For example

v
4
2
2
2nd
v
4

Keystrokes for TI-30X IIS
Keystrokes for TI-30X A
5
Example 1 Evaluate the expression. Give the
exact value, if possible. Otherwise, approximate
to the nearest hundredth. You may use a
calculator for this section.
2nd
8
v

What is the positive square root of 8?
Keystrokes for TI-30X IIS
6
Example 1 Evaluate the expression. Give the
exact value, if possible. Otherwise, approximate
to the nearest hundredth. You may use a
calculator for this section.

v
8
What is the positive square root of 8?
Keystrokes for TI-30X A
7
Evaluate the expression. Give the exact value,
if possible. Otherwise, approximate to the
nearest hundredth. You may use a calculator
for this section.
Example 2
What is the negative square root of 11?
Example 3
What is the positive and negative square root of
1.69?
8
To compare real numbers, find a decimal
approximation for each number and then compare.
The three dots are an ellipsis. In math, an
ellipsis is used to indicate that the numbers
continue in the same pattern.
The inequality symbol points to the smaller value!
9
Replace each with lt, gt, or to make a
true statement.
Example 4
Example 5
Example 6
Example 7
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Order from least to greatest.
Example 9
Example 8
Remember To compare real numbers, find a
decimal approximation for each number and then
compare.
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1-9 Coordinate Plane
All coordinate plane graphs must be completed on
grid paper.
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A coordinate plane is formed by two real number
lines that intersect at a right angle at the
origin. The horizontal axis is the x-axis and the
vertical axis is the y-axis.
y










I
II
The coordinate plane is divided into four regions
called quadrants.

x
IV
III
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Each point in a coordinate plane corresponds to
an ordered pair of real numbers.
(2,3)











The first number identifies the x-coordinate
and the second number identifies the y-coordinate.
x
y
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(3,4).
Graph the coordinate











The first number identifies the x-coordinate
and the second number identifies the y-coordinate.
x
y
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Example 1 Graph the coordinate
(4,2).
The first number identifies the x-coordinate
and the second number identifies the y-coordinate.










x

y
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Example 2 Graph and label the coordinates in the
same coordinate plane
A (3,1), B (4,0), C (5,2), D (2,4), E (0,3),
F (0,0).










E


C
B


x
F

A

D
y
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Example 3 In which quadrant or on which axis
does each ordered pair lie?

• A.
• B.
• C.
• D.
• E.
• F.
• G.
• H.

IV
E

H
x-axis II IV y-axis origin III I


C
B


F
x

A
G


D
y
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Example 4 Write the coordinates of each point.
D

A B C D E F G
Coordinates are written as ordered pairs. You
must use parentheses!
(3,2)










G

(4,0) (5,2) (2,4) (0,3) (0,0) (4,3)
B
F


x


C
A

E
y
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Homework
1-A13 Pages 50-52 2227,38-41,56-59,73-75.
(Scientific calculators OK).