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1.find the sum of 0.0333... and 0.444....
 
 

Asked by alok 13th September 2015, 9:19 PM
Answered by Expert
Answer:

C o n s i d e r space t h e space n u m b e r s comma space 0.03333... space a n d space 0.44444... L e t space x equals 0.03333.... rightwards double arrow 100 x equals 3.3333... space space space space space space left parenthesis 1 right parenthesis a n d 10 x equals 0.333333.... space space space space space space space left parenthesis 2 right parenthesis S u b t r a c t i n g space e q u a t i o n space left parenthesis 2 right parenthesis space f r o m space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma 90 x equals 3 rightwards double arrow x equals 3 over 90 space space space space space space open parentheses 3 close parentheses L e t space y equals 0.44444..... space space space space space left parenthesis 4 right parenthesis rightwards double arrow 10 y equals 4.4444.... space space space space space space space left parenthesis 5 right parenthesis S u b t r a c t i n g space e q u a t i o n space left parenthesis 4 right parenthesis space f r o m space e q u a t i o n space left parenthesis 5 right parenthesis comma space w e space h a v e comma 9 y equals 4 rightwards double arrow y equals 4 over 9 space space space space space space space space space space space space space space space space space space space space space space space open parentheses 6 close parentheses W e space n e e d space t o space f i n d space t h e space s u m space x plus y. T h u s comma space f r o m space e q u a t i o n s space left parenthesis 3 right parenthesis space a n d space left parenthesis 6 right parenthesis comma space w e space h a v e comma space x plus y equals 3 over 90 plus 4 over 9 space space space space space space space space space space equals 3 over 90 plus 40 over 90 space space space space space space space space space space equals 43 over 90 rightwards double arrow space 0.03333... space plus 0.44444... equals 43 over 90

Answered by Expert 14th September 2015, 6:03 PM
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