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Showing posts with the label Number system
Properties of Irrational Numbers
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1. Irrational numbers satisfy the commutative, associative and distributive laws for addition and multiplication. 2. (i) Sum of two irrationals need not be an irrational. Example: Each one of (2 + √3 ) and (3 - √3 ) is irrational. But, (2 + √3 ) + (3 - √3 ) = 5, which is rational. (ii). Difference of two irrationals need not be an irrational. Example: Each one of ( 4 + √5 ) and ( 2 + √5 ) is irrational. But, ( 4 + √5 ) - ( 2 + √5 ) = 2, which is rational. (iii). Product of two irrationals need not be an irrational. Example: √5 is irrational. ...
Real Numbers | Properties
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Real Numbers A number whose square is non-negative, is called a real number. Example: All rational and irrational numbers are real numbers. Addition Properties of real numbers: 1. Closure Property : The sum of two real numbers is always a real number. Example : Two real numbers are 1 and √ 2 , then (1 + √ 2) is a real number. 2. Commutative Property : a and b are two real numbers, then a + b = b + a Example : two real numbers are (2 + √3) and (2 – √3) , then (2 + √3) + (2 – √3) = 4 (2 – √3) + ( 2 + √3) = 4 Then...
Rational Numbers & Irrational Numbers | Examples
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Rational Numbers The numbers of the form a/b, where a and b are integers and b ≠ 0 are known as rational numbers. Example: 1/2, -4/5, 0, -1, 2 etc. or A number which can be expressed as a terminating decimal or repeating decimal , is called a rational numbers. Example: 5/3 = 1.666666....... = 1. 6 16/45 = 0.355555 ...... = 0.3 5 etc. Important result all natural numbers, whole numbers and integers are rational numbers. We can understand above terms with a picture diagram. Irrational Numbers A number which can neither be expressed as a terminating decimal nor a repeating decimal , is called an irrational number. Thus, non-terminating, non-repeating decimals are irrational numbers. Examples : Type 1. 0.2020020002....... , 0.4040040004...... etc. are a non-terminating and non-repeating decimal, therefore these are irrational number. Type 2 : If n is positive which is not a perfect squa...
What is Decimal Numbers? Terminating and Non-terminating | Recurring and Non-recurring decimal
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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 ...
Properties of Integers with examples
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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 ...
Definition of Integers - Positive & Negative Integers | jmathslearning
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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 ≠ ...
Properties of Whole numbers with examples
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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, ...
What is whole numbers | Definition, Even & Odd Numbers
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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 with examples
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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 thr...
What is natural numbers | Definition, Prime & Even Numbers
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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 num...