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About Real Numbers

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REAL NUMBERS- Real numbers  are simply the combination of R ational and Ir rational numbers  in the number system. A real number is any positive or negative number. Real numbers that include decimal points are also called floating point numbers, since the decimal "floats" between the digits. (i)Rational Numbers:- Can be expressed as the quotient of two integers (i.e, fraction ) in p/q form where p is numerator and q is denominator,such that  denominator is not zero. rational number can be integers, repeating decimal etc. IMP:- every fraction is not a rational number because fractions can contain irrational number such as. 2/√3 or √5/8. So all fractions are not rational number and every rational number is not fraction.                                       (ii) Irrational Numbers :- Can not be expressed as the quotient of two integers (i.e, a...
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Multiplication Properties of Real Number

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Multiplication Properties of Real Number 1)  Closure Property of Multiplication a × b  is a real number If you multiply two real numbers, the product is also a real number. Example:  6 × 5 = 30   where 30  (the product of 6 and 7) is a real number. 2)  Commutative Property of Multiplication               a × b = b × a  if you multiply two real numbers in order,the product will always be the same or equal. Example: 3 × 4 = 4 × 3 = 12 3)Associative Property of Multiplication                                               (a × b) × c = a × (b × c) If you are multiplying three real numbers, the product is always the same regardless of their grouping.   Example :  (5 × 2) × 4 = 5 × (2 × 4) = 40 4)  Multiplicative Identity Property of Multi...
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Addition Properties Of Real Numbers

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Addition Properties Of Real Numbers:-   (i) The Closure property:- Real numbers are   closed   under addition, subtraction, and multiplication. That means if   a   and   b   are real numbers, then   a + b   is a unique real number, and   a. b   is a unique real number. For Example:-  3 and 11 are real numbers. 3+11=14 and 3.11=33 notice that 14 and 33 both are real numbers. (ii)Commutative property Addition:- a+b=b+a if you add two real number in any order the sum will always be the same or equal. Example:- 3+7=7+3= 10 (iii)Associative property of addition:- (a + b) + c = a + (b + c) If you are adding three real numbers, the sum is always the same regardless of their grouping. Example:- (2+4)+1=2+(4+1)=7 (iv)Additive identity property of addition:- a + 0 = a If you add a real number to zero, the sum will be the original number itself. Example:- 5+0=0+5=5 (v...
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