Types of Numbers( Real numbers,Natural numbers,Whole numbers etc)
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June 27, 2016 |
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Types of Numbers
Real numbers: Real numbers comprise the full spectrum of numbers.
They can take on any form – fractions or whole numbers, decimal points
or no decimal points. The full range of real numbers includes decimals
that can go on forever and ever without end.
They can take on any form – fractions or whole numbers, decimal points
or no decimal points. The full range of real numbers includes decimals
that can go on forever and ever without end.
For Example: 8, 6, 2 + 
, 3/5 etc.
, 3/5 etc.
Natural numbers: A natural number is a number that comes naturally.
Natural Numbers are counting numbers from 1, 2, 3, 4, 5, ……..
Natural Numbers are counting numbers from 1, 2, 3, 4, 5, ……..
Whole numbers: whole numbers are just all the natural numbers plus zero.
For Example: 0, 1, 2, 3, 4, 5, and so on up to infinity.
Integers: Integers incorporate all the qualities of whole numbers and their opposites
(or additive inverses of the whole numbers) .
Integers can be described as being positive and negative whole numbers.
(or additive inverses of the whole numbers) .
Integers can be described as being positive and negative whole numbers.
For Example: … –3, –2, –1, 0, 1, 2, 3, . . .
Rational Numbers: All numbers of the form p/q where p and q are integers
(q ≠ 0) called Rational numbers.
(q ≠ 0) called Rational numbers.
For Example: 4, 3/4, 0, ….
Irrational Numbers: Irrational numbers are the opposite of rational numbers.
An irrational number cannot be written as a fraction,
and decimal values for irrational numbers never end and do not have a repeating
pattern in them. ‘pi’ with its never-ending decimal places, is irrational.
An irrational number cannot be written as a fraction,
and decimal values for irrational numbers never end and do not have a repeating
pattern in them. ‘pi’ with its never-ending decimal places, is irrational.
For Example: 
Even Numbers: An even number is
one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.
one that can be divided evenly by two leaving no remainder, such as 2, 4, 6, and 8.
Odd Numbers: An odd number is one that does not divide evenly by two,
such as 1, 3, 5, and 7.
such as 1, 3, 5, and 7.
Prime Number: A prime number is a number which can be divided only by 1 and itself.
The prime number has only two factors, 1 and itself.
The prime number has only two factors, 1 and itself.
For example: 2, 3, 7, 11, 13, 17, …. are prime numbers.
Composite Number: A Composite Number is a number which can be divided evenly.
Any composite number has additional factors than 1 and itself.
Any composite number has additional factors than 1 and itself.
For example: 4, 6, 8, 9, 10 …..
Co-primes or Relatively prime numbers: A pair of numbers not having any common
factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
factors other than 1 or –1. (Or alternatively their greatest common factor is 1 or –1)
For Example: 15 and 28 are co-prime, because the factors of 15 (1,3,5,15) , and the factors
of 28 (1,2,4,7,14,28) are not in common (except for 1) .
of 28 (1,2,4,7,14,28) are not in common (except for 1) .
Twin Primes: A pair of prime numbers that differ by 2 (successive odd numbers that are
both Prime numbers) .
both Prime numbers) .
For Example: (3,5) , (5,7) , (11,13) , …
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