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Question Number 122649 by mathocean1 last updated on 18/Nov/20

B y d i v i s i n g a n i n t e g e r a b y

i n t e g e r b w e f i n d t h e r e s u l t :

0.285714285714 \dots f o l l o w e d

b y a g r o u p o f 6 d i g i t s : 285714

w h i c h i s r e p e a t e d i n d e f i n i t e d .

d e t e r m i n a t e t h e f r a c t i o n \frac{a}{b}

Commented by mr W last updated on 18/Nov/20

0.285714 \dots = x

285714 + x = 100000 x

285714 = 999999 x

x = \frac{285714}{999999} = \frac{2}{7} = \frac{a}{b}

Commented by mathocean1 last updated on 18/Nov/20

t h a n k y o u v e r y m u c h s i r

Answered by liberty last updated on 19/Nov/20

l e t p = 0.285714285714 \dots

\Rightarrow 1000000 p = 285714.285714 \dots

s u b t r a c t (2) b y (1)

999999 p = 285714 \Rightarrow p = \frac{285714}{999999} = \frac{2}{7}

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