NUMBER SYSTEMIn mathematics, a 'number system' is a set of numbers (in the broadest sense of the word), together with one

or more operations, such as addition or multiplication.

Examples of number systems include: natural numbers, integers, rational numbers, algebraic numbers, 

real numbers, complex numbers and prime numbers

DIGIT & NUMBERSAll digits are numbers but all numbers are

not digit. Two or more digit makes a number.

NATURAL NUMBERS (N)

The positive (+) integer which are used for counting and ordering is called natural numbers. It is denoted by N or .

For example, N= {1, 2, 3, 4 ………….. }

Properties: Natural numbers start from 1. There is no highest number in natural number. i.e.; The addition and multiplication of two natural

numbers is also natural a number. The subtraction and division of two natural

numbers may be natural number or not may be.

PRIME NUMBER

The number which is divisible by 1 and itself only is called prime number.

For example: 2, 3, 5, 7, 11, 13 … Write down the difference between the highest and

lowest prime numbers which are lies 18-44?

Solution:

The prime number which are lies 18-44 is = 19,23,29,31,37,41,43

Here, the highest prime number is = 43 and the lowest prime number is = 19

Therefore, the difference is = 43-19

= 24

COMPOSITE NUMBER:

The number which is divisible not only by 1 and itself but also other numbers is called Composite number.

For example, 4, 6, 8, 10, 12…

EVEN NUMBER & ODD NUMBER:

Those natural numbers are divisible by 2 is called even number. It is denoted by 2N.

For example, {2, 4, 6, 8, 10…} Those natural numbers are not divisible by 2 is

called odd number. It is denoted by (2N+1). For example, {3, 5, 7, 9, 11…}

RATIONAL NUMBERS (Q)

The number which can be expressed in the form where p is any integer and q is an integer but not equal to zero is called a rational number. To state it formally

The set Q={……,-5,-4,-2,0,3/7,5/8,2,7…..}.

For examples, 3 = 3/1, -7 = -7/1 …

 

Rational numbers can be represented by decimals.

The decimal of some fractions are terminating or finite. For examples, ½=0.5, 2/5= 0.4 and 2/8= 0.25 etc.

 

The decimal of some fractions are non terminating or infinite but repeating. For example, 1/3= 0.333333333… = 0.3, 5/11= 0.45454545… = 0.45 etc.

IRRATIONAL NUMBERS

The numbers which cannot be expressed in the form , where and p, q are both integers, are called irrational numbers.

For examples:

are irrational numbers. The decimals irrational numbers are non-

terminating and non-repeating. For example, 2.2502469528…., 0.36458125…..etc are irrational numbers.

,2 ,2 ,2 ,2 ,2