how to find  rational numbers  when  the given no. is non-terminating recurring form.......

Asked by eeshan.nk | 17th May, 2016, 05:55: PM

Expert Answer:

S u p p o s e space t h e space g i v e n space n u m b e r space i s space 0.33333.....
T h i s space i s space a space n o n minus t e r m i n a t i n g space a n d space r e c u r r i n g space d e c i m a l.
L e t space x equals 0.333333..... space space space space space space space left parenthesis 1 right parenthesis
N o w space 10 x equals 3.333333..... space space space space space space space left parenthesis 2 right parenthesis
S u b s t r a c t i n g space e q u a t i o n space left parenthesis 1 right parenthesis space f r o m space e q u a t i o n space left parenthesis 2 right parenthesis comma space w e space h a v e comma
10 x minus x equals 3.33333.... negative 0.3333333.....
rightwards double arrow 9 x equals 3
rightwards double arrow x equals 3 over 9
rightwards double arrow x equals 1 third
T h u s comma space f r a c t i o n a l space f o r m space o f space 0.333333.... space i s space 1 third

Answered by Vimala | 19th May, 2016, 11:52: AM

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