1.3
Positive & Negative Real Numbers
Homework: Odds 1-57
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·Set- a collection of objects
·Integers-
the set which includes the natural numbers and their opposites and zero
(Show on number line.)
·Set
notation for Integers-
*Notice: Written in ascending order from smallest to largest.
Decide whether each phrase is represented by a
negative integer, a positive integer, or 0:
The check for $25
bounced.
-25
5 under
par
-5
12 over
par
+12
par
0
700 feet below sea
level
-700
3582 feet above sea
level
+3582
The store broke
even.
0
5 degrees below
zero
-5
·Rational
Numbers- the
set which includes integers, fractions, and decimal numbers (terminating or
repeating)
(Show on number line.)
·Set
notation for Rational Numbers-
·Irrational
Numbers- the
set which includes decimal numbers that neither terminate nor repeat
Ex. 
To put irrational numbers on the number line, for example 
,
use the calculator to get an approximation 
.
*Notice: This number is only an approximation since an irrational number is
a decimal number that never terminates or repeats.
(Show on number line.)
Summary of sets:
Irrational Numbers: 
Rational Numbers: all other numbers
Real Numbers: Irrational + Rational
Compare numbers with respect to their position on
the number line using
Examples: Compare 3 to
4: 3 < 4 Compare
–3 to –4: -3 > -4
(Show on number line.)
*Notice: The smaller number is the number that is farther to the left on
the number line.
·The
absolute value of a number represents how far the number is from 0.
Examples: 
Examples: How do the absolute values
compare? Be careful!
Compare 
: 
because
–3 is 3 units from 0 and –4 is 4 units from 0.
Examples: How do fractions compare? Use
the calculator to change to decimal numbers.
Compare 