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Decimal Number Decimal numbers are numbers that are written according to their place value. The decimal point is used to separate whole part from number value less than one.A symbol is used " . ", this is called decimal point. Example: 65.894 where 65 is a whole part and 894 is a fractional part. Type of Decimals 1. Terminating Decimals  2. Non-terminating Decimals 1. Terminating Decimals Every fraction a/b can be expressed as a decimal. If the decimal expression of a/b terminates i.e. comes to end, then the decimal so obtained is called a terminating decimal. Example: 1/2 = 0.5                   5/4 = 1.25                 13/5= 2.6 Thus, each of the numbers 1/2, 5/4 and 13/5 can be expressed in the form of a terminating decimal. 2. Non-terminating Decimals While expressing a fraction in the form of decimal, when we perform division we get some remainder. If the division process does not end i.e. remainder is not equal to zero, then such dec

Properties of  Integers Addition Properties of Integers: 1. Closure Property:    The sum of two Integers is always an Integers. Example: Let two Integers are -4 and -6 then                            (-4) + (-6) = (-10) is an Integer. 2. Commutative Property:  Let a and b are two Integers, then                                 a + b = b + a   Example: Let two integers are -5 and 6 then                    (-5) + 6 = 1                   6 + (-5) = 1   then        (-5) + 6 = 6 + (-5)  Hence commutative property is verified 3. Associative Property:   Let a, b and c are three integers, then                                             a + ( b + c) = (a + b ) + c Example: Let three integers are 3, 5 and (-6) then                   3 + { 5 + (-6) } = 3 + {5 - 6 } = 3 + (-1) = 2                   {3 + 5 } + (-6)  =  8 - 6  = 2  then          3 + { 5 + (-6) } =   { 3  + 5 } + (-6)  Hence Associative property is verified 4. Existence of Additive Identity: 

Integers An  integer  is a number that can be written without a fractional component that. It can be positive, negative or zero.It is denoted by " ℤ ". ℤ  = { .......  –3,  –2,  –1, 0, 1, 2, 3, 4, 5, ........ } Type of Integers  1. Positive     Integers 2. Negative       Integers 3. Non-negative Integers 1. Positive Integers Whole numbers greater than zero are called Positive Integers . It is also called Natural Numbers   and denoted by " ℤ + ".  ℤ +  = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ....... } 2. Negative Integers A  negative integer  is an  integer  to the left of zero on the number line. It is less than zero.It is denoted by " ℤ − ". ℤ −   = { ........... , −7,  −6,  −5,  −4,  −3,  −2,  −1} 3. Non-Negative Integers An  integer  that is either 0 or positive. It is also called Whole Numbers and denoted by " ℤ ≠  ". Some Authors use symbol "  ℤ * ".   ℤ ≠  = { 0,  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, .......

Properties of Whole Numbers Addition Properties of Whole Numbers: 1. Closure Property:   The sum of two whole numbers is always a whole numbers. Example: Let two whole numbers 5 and 7 then                            5 + 7 = 12 is a whole number. 2. Commutative Property:  Let a and b are two whole numbers,                                                a + b = b + a  Example: Let two whole numbers are 5 and 6 then                   5 + 6 = 11                   6 + 5 = 11   then        5 + 6 = 6 + 5  Hence commutative property is verified 3. Associative Property:   Let a, b and c are three whole numbers,                                             a + ( b + c) = (a + b ) + c Example: Let three whole numbers are 3, 5 and 6 then                   3 + ( 5 + 6 ) = 3 + 11 = 14                   (3 + 5 ) + 6  =  8 + 6  = 14  then          3 + ( 5 + 6 ) =   (3  + 5 )  + 6  Hence Associative property is verified 4. Existence of Additive Identity:   For any whole n

Whole Numbers All natural numbers together with zero form the collection of all whole numbers. It is denoted by "W" W = { 0,1,2,3,4,5,6,7,8,9,10, ............... } Type of Whole Numbers 1. Even Numbers 2. Odd  Numbers 1. Even Numbers A number which is divisible by 2, it is called even number. It is denoted by "E".  E = { 0,2,4,6,8,10,12,14,16,18,20,  ........ } 2. Odd Numbers A number which is not divisible by 2, it is called odd number. It is denoted by "O". O = { 1,3,5,7,9,11,13,,15,17,19,21, ....... }  We can understand whole numbers from a picture

Properties of Natural Numbers Addition Properties of Natural Numbers: 1. Closure Property:   The sum of two natural numbers is always a natural numbers. Example: Let two natural numbers 2 and 5 then                            2 + 5 = 7 is a natural number. 2. Commutative Property: Let a and b are two natural numbers,                                                a + b = b + a  Example: Let two natural numbers are 5 and 7 then                   5 + 7 = 12                   7 + 5 = 12   then        5 + 7 = 7 + 5  Hence commutative property is verified 3. Associative Property:   Let a, b and c are three natural numbers,                                             a + ( b + c) = (a + b ) + c Example: Let three natural numbers are 3, 5 and 6 then                   3 + ( 5 + 6 ) = 3 + 11 = 14                   (3 + 5 ) + 6  =  8 + 6  = 14  then          3 + ( 5 + 6 ) =   (3  + 5 )  + 6  Hence Associative property is verified 4. Existence of Additive Identity:

Natural Numbers Counting numbers are known as natural numbers.  It is denoted by "N"  N = { 1,2,3,4,5,6,7,8,9,10,11,12,13, ....... } Type of Natural numbers  1. Prime numbers  2. Composite numbers   1. Prime numbers A number which have only two prime factor, it is called a prime numbers. It is denoted by "P".  P = { 2,3,5,7,11,13,17,19, ....... } e.g. "2" have two factors 1 and itself .  Similarly some other examples written below :                     3 -> 1 and 3                     5 -> 1 and 5                     7 -> 1 and 7                                                      11 -> 1 and 11 etc.  2. Composite numbers A numbers which have more than two factors, it is called a composite numbers.      { 4,6,8,9,10,12,14,15,16,18, ...... } e.g. "4" have more than two factors 1, 2 and 4 Similarly some other examples written below :                     6 -> 1, 2, 3 and 6