Transcript Real Number System a.

Section 1-3 Explore Real Numbers
SPI 12A: Order a given set of rational numbers
TPI 12F: Explore various representations of Absolute Value
Objectives:
• Investigate the Real Number System
• Classify and Compare Numbers
Real Number System
Irrational Numbers
Rational Numbers
Coordinate Plane
y
Integers
Whole Numbers
Natural Numbers
Real number line
X
Real Number System
Rational Numbers
Any number that can be written
in the form  where a and b are
integers and b is not equal to 0.
(Can be terminating, such as 6.27
.. Or .. Repeating like 8.222….)
Irrational Numbers
Any number that can not be
written in the form of .
(Nonrepeating & non-terminating)
Natural Numbers
1, 2, 3, …
1 2 3 4
5 6 7 8 9 10 11
Whole Numbers
0, 1, 2, 3, …
0 1 2 3 4
5 6 7 8 9 10 11
Integers
. . . -3, -2, -1, 0, 1, 2, 3, …
-3 -2 -1 0 1 2 3 4
Name the set of numbers to which each number belongs
a. - 3
Rational, integer
b. 3.28
Rational
c. 
Irrational
d. .
Rational (its repeating)
Practice: Determine the set of numbers that is reasonable for a
given situation.
ALGEBRA 1 LESSON 1-3
1. Which set of numbers is most reasonable for displaying
outdoor temperatures?
integers
2. Which set of numbers is most reasonable for the number of
students who will go on a class trip?
whole
3. Which set of numbers is most reasonable to determine the
height of a door? rational
4. Is the following statement true or false. If false, give a
counterexample. “All negative numbers are integers.”
False, because a negative number can be a fraction
such as ½, which is not an integer.
Comparing Numbers and Ordering Fractions
Inequality: mathematical sentence that compares the value
of 2 expressions.
a<b
a>b
a=b
ab
ab
a≠b
a is less than b
a is greater than b
a is equal to b
a is less than or equal to b
a is greater than or equal to b
a is not equal to b
Compare a set of rational numbers using a number line and
inequalities.
Write -1/8, 1, ¾, -1/2, -1 from least to greatest.
-1
-1/2
-1/8 0
3/4
-1 < -1/2 < -1/8 < ¾ < 1
1
Order Fractions by Converting to Decimals
Step 1: Convert fraction by dividing numerator by denominator
Step 2: Compare the decimals:
- the smaller number is the least
(Pay attention to negative values)
Step 3: Convert back to fractions and write in order
Write – 3 , – 7 , and – 5 , in order from least to greatest.
4
12
8
– 3 = –0.75
4
– 7 = –0.583
12
– 5 = –0.625
8
Write each fraction as a decimal.
-0.75 < -0.625 < -0.583
Write 1/12, -2/3 amd -5/8 in order from least to greatest.
Step 1: Convert to decimal:
1/12 = .083
-2/3 = -.666666667
-5/8 = -.625
Step 2: Order decimals
-.666666667 < -.625 < .083
Convert back to fraction
-2/3 < -5/8 < 1/12
Absolute Values
Opposites
• Two numbers that have the same distance from zero on a number
line but lie in opposite directions
• Example: 1 and -1, 450 and -450, -1/2 and ½
Absolute Values
• The distance of a number from zero on a number line
• Written as a number enclosed by 2 vertical lines
• Example: |3| and |-3| both have a value of 3
Modeling Absolute Value
If you are at home and decide to take a ride on your
motorcycle to your friends house, which is ten miles away.
Your friend lives in the red house.
How many miles did you travel away from your home?
You and your friend decide to go to the store, the yellow
house. How far is it from your friends house to the store?
-10
0
Home
10
Practice Absolute Value
Find each absolute value.
a. |–2.5|
b. |7|
–2.5 is 2.5 units from 0
on a number line.
7 is 7 units from 0
on a number line.
|–2.5| = 2.5
|7| = 7
c. |5 - 7|
-2 is 2 units from 0
on a number line.
|–2| = 2