Method 2: Conversion of recurring decimal to p/q form .
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CONVERSION OF RECURRING DECIMAL TO P/q (rational ) form ,where p & q belongs to integers and q is not equal to zero आवर्ती दशमलव को p/q ( परिमेय संख्या) के रूप में बदलना ।
METHOD : 1 आवर्ती दशमलव को p/q (परिमेय संख्या ) के रूप में बदलने का तरीका निम्न प्रकार है - Step 1 :- write given number except point and recurring and subtract the number which is before recurring (At the place of numerator) रेकरिंग और दशमलव को छोड़कर दिए गए संख्या को अंश (p) के स्थान पर लिखें तथा उनमें से रेकरिंग से पहले की संख्या को घटा दें । STEP 2 :- In the denominator, write that much 9 instead of how many digits are under recurring and that much zero (0) instead of how many numbers are between recurring and the point. If there is no digits between point and recurring sign then do not write zero . हर (q ) के स्थान पर उतना 9 लिखे जितने अंकों के ऊपर रेकरिंग है और उतना शून्य(0)लिखें जितने अंक रेकरिंग और दशमलव के बीच मे हैं । point और recurring चिन्ह के बीच यदि कोई अंक नही हो तो शून्य नही लिखें । STEP 3 :- Calculate and write it in the simplest form . Finally you will get the given no in the rational form .(calcul...
REAL NUMBERS (वास्तविक संख्याएँ )
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)
DECIMAL EXPANSION (दशमलव प्रसार)
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) ...
NUMBER SYSTEM
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...
NUMBER SYSTEM
1. NATURAL NO.(N) : All numbers in the count that begin at 1 and go to infinity , is called natural numbers. eg. 1,2,3,4,...........infinity . N={1,2,3,4,5,.......} ; A set of natural no. 2. WHOLE NO.(W): All numbers in the count that begin at 0 (zero) and go to infinity ,is called whole numbers. eg. 0 ,1 ,2, 3, ..........infinity . W={0,1,2,3,4,..........} ; A set of whole no. Note : N c W 3. INTEGERS (I or Z): when the negative numbers ,zero and positive numbers are represented on a number line from left to right respectively then these numbers are called integers. ____________________________________ ' ' ' ' ' ' ' ' eg. .........-4 , -3 ,-2 ,-1 , 0 , 1 , 2 ,3 ,......... I or Z={.........-4,-3,-2,-1,0,1,2,3,4,......} ; A se...