BSEB MATHEMATICS

REAL NUMBERS (वास्तविक संख्याए)  : A number which is either rational or irrational   , is called real number.It is denoted by  'R'.   " वैसी संख्या जो या तो परिमेय हो या अपरिमेय , वास्तविक संख्या कहलाती है । " Eg. -2 , 4/5 , √2 , 0 , π    etc  Note: N c W c I c Q c R Types of Real Numbers : 1. Rational  No.(परिमेय संख्या ) 2. Irrational  No.(अपरिमेय संख्या)  * 1.) Rational no. को दो भागों में बंटा गया है -- i) Integers ( पूर्णांक संख्याएँ ) ii) Fraction  ( भिन्न ) *    Integers (पूर्णांक संख्या ) को तीन भागों में बंटा गया है - i) negative integer ऋणात्मक पूर्णांक  ii) Zero (शून्य) Iii) positive integer (धनात्मक पूर्णांक)

It is of two types mainly. Terminating Decimal Expansion(शान्त दशमलव प्रसार)      2.  Non-terminating decimal                                   expansion(अशान्त दशमलव प्रसार )                         Decimal expansions                                    _________________|__________________                 |                                                              |        Terminating                         Non-terminating (शांत)    ...

RATIONAL NO. :  A number of the form p/q , where  p and q both are integers and q not equal to Zero (0) is called a rational number.    The set of rational no . denoted by   Q  eg. 3/5 , 4/5 , -7/6 ,  0 , 1 , 2 , 3 , -6, -7 , etc  0=0/1 , 1=1/1 =p/q   Notes : a) N c W c I c Q  b) A rational no. P/q  is called in standard form if p and q have no common factor other than 1. eg. 20/36   (not in standard form) But 5/9 ( is in standard form )  or 20/36  both are divided by 4 and we get  5/9 hence it is in the standard form  because it has no common factor other than 1. C) All terminating decimals ( ie 3.42, 5.6, 2.5 5.0 etc ) are  rational numbers . d) All recurring decimals (ie 1.333..., 2.3333..., 0.121212...., 0.245245..., etc ) are rational numbers . e)Decimal form of a rational no. is either terminating or recurring. eg. 5/2 = 2.5      (Terminating)       7/2= 3.5...