Real Numbers
Section 0.1
TERMS you should know
 Set – A group or collection of objects
 Subset – A set of objects that are all members of







another set
Ellipsis (…) – The pattern continues
Empty set 0 – A set with no elements
Numerator – Top of a fraction
Denominator – Bottom of a fraction
Constant – A known value
Variable – A letter representing some unknown value
Coefficient – A known value multiplied by a variable
Types of numbers
Symbol
Name
Description
Examples
N
Natural
Counting
1,2,3,4,…
W
Whole
Zero & Natural Numbers
0,1,2,…
Z
Integers zero & positive and
…,-2,-1,0,1,…
negative counting numbers
Q
I
Rational Ratios of integers
(repeating or terminating
decimals)
Irrational Don’t repeat or terminate
R
Real
Rational and Irrational
-15, -¾, 0,
3.666, 5
3 ,1.5479 ... , 
Real Numbers
Real
Numbers
Rational Numbers
Integers
Whole Numbers
Natural Numbers
Irrational
Numbers
Rational or Irrational???
 Same as 4.5
9
 Terminates
2
 Rational Number
7
9
 Same as .777777777
 Repeats
 Rational Number
 If it can be written as a ratio of integers it is Rational
 Same as 4.582575695…
 Doesn’t repeat or terminate
21
 Irrational
 Remember all rational and irrational numbers are real
numbers
Rounding or Truncating
 Round 4.6769 to two decimal places
 4.68
 Truncate (cut off at) 4.6769 to two decimal
places
 4.67
Simplify using the order of operations
PEMDAS
2
3 ( 10 – 3 · 2 ) + 30 – 5
= 3 ( 10 – 6 ) + 30 – 5
= 3 ( 4 ) + 30 – 5
2
= 3 ( 4 ) + 30 – 25
= 12 + 30 – 25
= 42 – 25
= 17
2
Simplify using the order of operations
PEMDAS
-3(2x + 4y) – (3x + 7y)
-6x – 12y – 3x – 7y
-9x – 19y
5x
4  (  6)

5x
10

x
2
Add/Subtract the fractions
2

1
7
5
10
7

35
35
3
35
5x

3x
6
8
20 x

24
29 x
24
9x
24
1
2
4
3
5
1
2

9
3
2
10
27

6
6
37
6
Simplify
3
 7x 
4
3
1
x 5
4

4
28
x
4
29
4
29
4
x
x
1
4
14
4
7
2
3
4
x
20
4

3
4
Simplify
3x

14
7
4
2
3
7

x
9
1
3
14
4

3

2
3

31
4

2x
3

14
3

4
31

56
93
Evaluate the algebraic expression
a = 2, b = -3, c = -4
2a – 5b²
2(2) – 5(-3) ²
2(2) – 5(9)
4 – 45
-41
a b
c b
2

2  3
(  4 )  (  3)
2

6
16  3

6
19
Absolute value- distance from zero
|-2|
=2
|-2+7|
=|5|
=5