Tipes of Numbers

 Tipes of Numbers

★Numbers

★ Natural Numbers(N)

★ Whole Numbers(W)

★ Integers(Z)

★ Even Numbers

★ Odd Numbers

★ Rational Numbers

★ Mixed Numbers

★ Irrational Numbers

★ Real Numbers

★ Composite Numbers

★ Prime Numbers

★ Twin-Prime Numbers

★ Co-Prime Numbers

★ Face Value and Base Value

★ BODMAS Rule

Natural Numbers(N):

(Positive Integers) 1,2,3,4,‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Whole Numbers(W):

(set of all natural numbers and 0) 0,1,2,3,4,5,‐‐‐‐‐‐‐‐‐‐‐‐‐‐ 

Integers(Z):

 ‐‐‐‐‐-3,-2,-1,0,1,2,3,4,5,‐‐‐‐‐‐‐‐‐

Even Numbers:

2,4,6,8,,‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Numbers are exactly divisible by 2. These numbers are end with even number or zero.

Odd Numbers:

1,3,5,7,8,‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Numbers are not exactly divisible by 2. These numbers are end with odd number.

Sum of any two odd number is always an even number.

Product of any two odd numbers always an odd number.

Rational Numbers:

Numbers which can be expressed in the form of p⁄q, where p and q both are integers, and q is a non-zero integer.

A number expressed in the form of p ÷ q is also called a fraction, where p is numerator and q is denominator.

A fraction when converted into decimal, gives finite or recurring digits after decimal sign.

Ex: 1⁄3, 1⁄2, 7⁄4

Mixed Numbers:

Numbers which consists of a whole number and a fraction.

Ex: 31⁄4, 52⁄7, 46⁄17, etc.

Irrational Numbers:

Numbers which cannot be expressed in the form of p ÷ q where p and q both are integers i.e., the numbers which are not Rational.

These numbers when converted into decimal, give infinite and non-recurring digits after decimal sign.

Ex: π , √ 2  , √ 3  , √ 27 

Real Numbers:

Real Numbers are combination of rational and irrational numbers.

Complex or imaginary Numbers:

These numbers are written as a+bi where i2=-1.

Composite Numbers:

The number which have more than two factors.

Ex: 4,6,8,9.

Prime Numbers:

A number which is not divisible by any number other than 1 and itself.Such numbers have only two factors,the number itself and 1.

Ex: 2,3,5,7,11,13,17,19.

1 is neither a prime number nor a composite number.

Product of any two prime numbers is always a composite number, since the product is divisible by both the prime numbers.

Twin-Prime Numbers:

Pairs of such prime numbers whose difference is 2.

Ex: 3 and 5, 11 and 13.

Co-Prime Numbers:

Co-Prime Numbers are those numbers which are prime to each other i.e., they don’t have any common factor other than 1.

Since these numbers do not have any common factor, their HCF is 1 and their LCM is equal to product of the numbers.

Co-prime numbers can be prime or composite numbers. Any two prime numbers are always co-prime numbers.

Ex1: 3 and 5 both numbers are prime numbers.

Ex2: 8 and 15 both numbers are composite numbers but they are prime to each other i.e., they don’t have any common factor.

Face Value and Base Value:

Face value is absolute value of a digit in a number.

Place value or Local value is value of a digit in relation to its position in the numbers.

Ex:  Face value and Place value of 9 in 12921 is 9 and 900.

BODMAS Rule:

Any simplification of an expression may involve various operations, these operations must be performed in the following order of preference.

B:Bracket:

If more than one type of brackets are found, they are operated in the following order,

First: (   ) line or bar bracket or vinculum bracket.

Second: (  ) small bracket.

Third: { } Mid bracket.

Forth: [ ] Large Bracket.

O(of): means multiplication but is operated before division.

D: Division.

M: Multiplication.

A: Addition.

S: Subtraction.

Note:

If sum of two numbers a and b is x and difference between the numbers is y.

then a = x+y⁄2 and

b = x-y⁄2

If on adding 9 to a two digit number (say xy), its digits are reversed.; Then units digit of the number exceeds its tens digit by 1. Similarly, if on adding 9a to a two digit number its digits are reversed, then units digit of the number exceeds its tens digit by a i.e., x+a = y

if digits are reversed on subtracting 9a from the number then x-a=y

Difference between two digits of the number is number added/subtracted÷ 9.

if on adding 99a to a three digit number (say xyz), its digits are reversed, then x+a = z

If digits are reversed on subtracting 99a from the number, then x-a = z.

If a composite number C, can be expressed as am × bn × cp‐‐‐‐‐, where a,b,c‐‐‐ are prime factors and m,n,p‐‐‐ are natural numbers, then total number of factors of C

= (m+1)×(n+1)×(p+1)‐‐‐‐

Total number of factors includes unity and the number itself.