Number System: Types of Numbers
Posted on : 19-11-2017 Posted by : Admin

The following are the details of various types numbers. Different types of numbers are used to deal with different situations hence each number type has it own importance.

Natural numbers

  • The numbers which are used in counting are called as natural numbers.
  • The set of natural numbers is denoted by the letter, N.

Where N= {1, 2, 3, 4…}

  • 1 is the smallest natural number.

natural numbers, N

Whole numbers

  • When zero is included in the set of natural numbers then they are called as whole numbers.
  • The set of whole numbers is denoted by the letter, W.

Where W= {0, 1, 2, 3, 4…}

  • All the natural numbers are also whole numbers.

Whole numbers, W, Zero

Facts about Whole Numbers

  • Number 0 is the first and the smallest of all whole numbers.
  • All natural numbers along with zero are called whole numbers.
  • Here is no last or greatest whole number since they are infinite.
  • All natural numbers are whole numbers. But all whole numbers are not natural numbers. For example 0 is a whole number but not natural number.
  • Each whole number is 1 more than its previous number.
 

Integers

  • When the negative numbers of all the natural numbers are included in the set of whole numbers, then they are called as Integers.
  • The set of integers is denoted by the letter, Z. The letter Z is taken from the German word zahlen which means to count.

Where Z= {…-4, -3, -2, -1, 0, 1, 2, 3, 4…}

  • Zero can never be a positive or negative integer.
  • The integers can further be divided into two types,

    * Positive integers: All the natural numbers are positive integers.

    Example: I+= {1, 2, 3, 4…}

    * Negative integers: All the negatives of natural numbers are negative integers.

    Example: I- = {-1, -2, -3, -4…}

    integers, z, positive, negative, zahlen,

    Rational numbers

    • The numbers which can be expressed in the form of p/q are called as rational numbers.

    Here p and q are integers and q is not equal to 0

    • The set of rational numbers are denoted by the letter Q.

    Where Q= {1/2, 1/3, 5/6, 7/2, 5, -2, 0…}

    Rational numbers, p/q form, Q

    Irrational numbers

    • The numbers which CANNOT be expressed in p/q form are called as irrational numbers.

    Here also p and q are integers and q is not equal to 0

    • The set of irrational numbers are denoted by the letter P.

    Where P= {√2, √3, √4, √5…}

    Irrational numbers, P, Square root, p/q

    Facts about Irrational Numbers

    • The sum of rational and irrational numbers is also an irrational number

    (Ex: 3+√2, 6+√4)

    • The difference of rational and irrational numbers is also an irrational number

    (Ex: 6-√2, 9-√4)

    • The product of rational and irrational numbers is also an irrational number

    (Ex: 2 x √2, 9 x +√4)



    Real numbers

    • Real numbers include both rational and irrational numbers. In other words, it includes all the natural numbers, whole numbers and also the integers.
    • The real numbers are denoted by the letter R.
    • Examples for real numbers are 2, 0, 5, -7, -10, ½, 1/6, 1.14, 1.789…

    Even numbers

    • The numbers which are divisible by 2 are called as even numbers. They are also the multiples of 2.
    • The set of even numbers is denoted by the letter E, Where E= {2, 4, 6, 8, 10…}
    • There are infinite even numbers

    Odd numbers

    • The numbers which are NOT divisible by 2 are called as odd numbers.
    • They are NOT multiples of 2.
    • The set of odd numbers is denoted by the letter O, Where O= {1, 3, 5, 7, 9…}
    • There are infinite odd numbers

    Prime numbers

    • The numbers which are divisible by 1 and the number itself are called as prime numbers.
    • The examples of prime numbers are 2, 3, 5, 7…

    Facts about Prime Numbers

    • Number 1 is not a prime number.
    • Number 2 is the only even prime number.
    • There are 25 prime numbers between 1 and 100. Out of these 15 are between 1 and 50 and remaining 10 are between 50 and 100.
     

    Co-prime numbers

    • Two natural numbers are called as co-primes if their Highest common factor (HCF) is 1.
    • Examples of pairs of co-primes are (7, 9), (15, 16) etc.
    • Co-primes are always written in pairs between the brackets.
    • It must be noted that the pair of co-prime numbers need not be prime numbers.

    Composite numbers

    • The numbers which are divided evenly by numbers other than 1 and itself are called as composite numbers.
    • For example, 9 can be divided evenly by 3 as well as 1 and 9, so 9 is a composite number. But 7 cannot be divided evenly except by 1 and 7, so is NOT a composite number. So it is a prime number.
    • Number 1 cannot be considered as the composite number.

    Consecutive numbers

    • Consecutive numbers are the series of numbers in which each number is greater than its preceding number by 1.
    • For example, 6, 7, 8 or 2, 3, 4 or 11, 12, 13, 14… etc.


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    Comments

  • Netra Solanki on Jun 23, 2018 at 07:03 am

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