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Number systems
Groups of Numbers
In doing arithmetic and algebra, we work with severalgroups o
f
numbers.
NATURAL or COUNTING NUMBERS: The numbers 1, 2,
3, 4, . . . are
called natural or counting numbers .
WHOLE NUMBERS : The numbers 0, 1, 2, 3, . . . are called
wholenumbers.
INTEGERS: The numbers . . .2, -1, 0, 1, 2, . . . are
calledintegers .
NEGATIVE INTEGERS : The numbers . . .3,2, -1 arecalled
negative integers .
POSITIVE INTEGERS : The natural numbers are sometimes
called th e
positive integers .
RATIONAL NUMBERS: Fractions, such as 3/2 or 7/8, are
called rational
numbers. Since a number such as 5 may be written as all
integers
are rational numbers .
IRRATIONAL NUMBERS : Another type of number is anirrational
number. Examples of irrational numbers are lj" and 7r .
REAL NUMBERS: Real numbers consist of all rational and
irrationa l
numbers. Typically most standardized exams use only real
numbers ,
which are the numbers you are used to using .
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PRIME NUMBERS : A prime number is a number that can be
evenly
divided by only itself and 1 . For example, 19 is a prime
numbe rbecause it can be evenly divided only by 19 and 1, but21
is not aprime number because 21 can be evenly divided by
other numbers ( 3and 7) . The only even prime number is 2 ;
thereafter, any even numbe rmay be divided evenly by 2 .
Zero and 1 are notprime numbers. Th efirst ten prime
numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29 .
ODD NUMBERS : Odd numbers are whole numbers not
divisible ,by 2 :1,3,5,7, . . .
EVEN NUMBERS : Even numbers are numbers divisible by
2: 0, 2, 4 ,
6, . . .
COMPOSITE NUMBERS: A composite number is a number
divisible b y
more than just 1 and itself: 4, 6, 8, 9, 10, 12, 14, 15, . .
.SQUARES: Squares are the result when numbers are
multiplied b y
themselves : (2 . 2 = 4), (3 3 = 9) ; 1, 4, 9, 16, 25, 36 . .
.
CUBES: Cubes are the result when numbers are multiplied b
y
themselves twice: (2 . 2 . 2 = 8), (3 3 . 3 = 27) ; 1, 8, 27
.
Signed Numbers (Positive Numbers and NegativeNumbers )Number
Lines
On a number line, numbers to the right of 0 are positive .
Numbers
to the left of 0 are negative, as follows .
