Download Real numbers

Algebra 2
1.1 Real Numbers and Number
Operations
Key Concepts 1 - 4
There are two main groups of
numbers
• Real numbers – those numbers used most
often in the real world and in algebra
Key Concepts 1 - 4
There are two main groups of
numbers
• Real numbers – those numbers used most
often in the real world and in algebra
• Imaginary numbers – also called complex
numbers, These are used to explore the
concepts of mathematics beyond our real
world
Different Types of Real Numbers
• Whole numbers – these are the counting
numbers, 0, 1, 2, 3, . . . Notice that they do
not include negative numbers
Different Types of Real Numbers
• Whole numbers
• Integers – These are the whole numbers
and the negative numbers,
. . . ,-3,-2,-1, 0, 1, 2, 3, . . .
Different Types of Real Numbers
• Whole numbers
• Integers
• Rational numbers – These are numbers that can
be written as ratios of integers. Numbers such as
½ and -4 since -4 can be written as
4
1
Different Types of Real Numbers
•
•
•
•
Whole numbers
Integers
Rational numbers
Irrational numbers – Those numbers that cannot
be written as ratios (fractions) such as 2
Different Types of Real Numbers
•
•
•
•
Whole numbers
Integers
Rational numbers
Irrational numbers – Those numbers that cannot
be written as ratios (fractions) such as 2
Some will argue that you can write this as a fraction by placing it above 1.
That is why we use the term ratio of integers. A ratio is a comparison of one
integer to another integer. The Square root of two is a non-repeating,
unending decimal number which can not be written since the decimal values
go on forever. So we use the symbol shown above for the square root of
two.
Different Types of Real Numbers
•
•
•
•
Whole numbers
Integers
Rational numbers
Irrational numbers
These four groups
can be found in the
chart on page 3 of the
textbook
Different Types of Real Numbers
•
•
•
•
Whole numbers
Integers
Rational numbers
Irrational numbers
Each of these groups are sub groups (or subsets) of the
set of real numbers. Some numbers can be found in all
of the first three sets listed (such as the number 2). If a
number is to be found in the first three sets, they are
never part of the fourth, the fourth set stands alone, but
all four subsets make up the set of real numbers.
Whenever you read “real numbers”
in the book, they are referring to a
number which can be found in any
of the four subsets we just looked
at. That means it could be a whole
number, a negative number, a ratio,
or an irrational number.
That also means that an answer of “No
real solution” refers to a number which
cannot be placed in any of these four
groups. A number such as the square
root of negative one is not a real
number. If my answer is the square root
of a negative number then I say,
“No real solution.”
The next topic addressed in this section is that of a
number line and placing real numbers on the number
line. Here are the basic facts about a number line.
-6
-4
-2
0
2
4
6