Download 1 - Daytona State College

Simply put, there are two basic categories of numbers in our number system: Real Numbers and Non-Real Numbers,
otherwise known as Imaginary Numbers. If you have not yet learned about imaginary numbers, all you need to know
at this time is that all numbers are real numbers EXCEPT imaginary numbers. Listed below are the real numbers:
Natural Numbers begin with the number one and continue infinitely in the positive direction:
, 58,, 9,
6, 10,
7, .8.,.
1, 2, 3, 1
4,, 5,2,6 3
, 7,
9, 10, 11, 12 . . .
Whole Numbers begin with the number zero and continue infinitely in the positive direction. Take note that
Whole Numbers begin with the number zero and continue infinitely in the positive direction. Take note that
0, 1, 2, 3,of5,natural
6 , 7, numbers
8, 9, 10, but
. . .include the number zero:
whole numbers are an extension
0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12 . . .
are all numbers on the number line from the negative infinity direction and continue infinitely in the
Integers
are all numbers on the number line from the negative infinity direction and continue infinitely in the
positive direction. Fractions, decimals, and irrational numbers are not integers. Integers include all
of the preceding numbers ( natural numbers and whole numbers ):
. . . - 10, - 9, - 8, - 7, - 6, - 5, - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, 5, 6, 7, 9, 10 . . .
Rational Numbers are integers, but in the form of ratios or fractions. A fraction is actually a ratio of two integers.
Repeating decimals, terminating decimals, and perfect square roots are considered rational
numbers because they can be converted or rewritten as ratios:
1
are numbers that cannot be written as a ratio4 or
example: non-repeating
decimals,
75
4 ,
√𝟗 for
or fraction,
= 3 or 31 , 0.75 = 100
⅜ , - ⅚, 0.66 or ⅔ ,
= ¾ , 0.142857142857 = 7
1
Irrational Numbers
are numbers that cannot be written as a ratio or fraction, for example: non-repeating decimals,
non-terminating decimals, and non-perfect square roots:
0.5196223 . . . ,
- 0.2145576 . . . ,
The Academic Support Center at Daytona State College (Math 1 pg. 1 of 2 )
√𝟕 = 2.64575131 . . . ,
π = 3.141592654 . . . ,
e = 2.718281845 . . .
Real Numbers vs Non-Real Numbers on the back
Following, are a few more examples of real numbers and one example of an imaginary number. Remember, all numbers
are real numbers , except imaginary numbers. Specific information about imaginary numbers can be obtained from
handout # 42 ( “Imaginary Numbers” ) on our math carousel.
Real Numbers
Natural Numbers:
Whole Numbers:
Non-Real Numbers
1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . .
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . .
Integers:
. . . - 4, -3, -2, -1, 0, 1, 2, 3, 4 . . .
Rational Numbers:
¾, -½,
0.333 or
⅓,
2
Everything else is a
REAL NUMBER
5
5 or 1 ,
25
√𝟒 = 2 or 1 , 0.25 = 100 =
Irrational Numbers:
Imaginary Numbers: 𝒊 = √−𝟏
¼
- 0.21455736 . . . ,
= 1.41421 . . . , π = 3.14592 . . .
0.51962814 . . . ,
√𝟐
The Academic Support Center at Daytona State College (Math 1 pg. 2 of 2
Revised 3 / 2011
JMay