By divising an integer a by integer b we find the result: 0.285714285714... followed by a group of 6 digits: 285714 which is repeated indefinited. determinate the fraction (a/b)


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Question Number 122649 by mathocean1 last updated on 18/Nov/20
$By divising an integer a by integer b we find the result: 0.285714285714... followed by a group of 6 digits: 285714 which is repeated indefinited. determinate the fraction (a/b)$
$B y d i v i s i n g a n i n t e g e r a b y$ $i n t e g e r b w e f i n d t h e r e s u l t :$ $0.285714285714 . . . f o l l o w e d$ $b y a g r o u p o f 6 d i g i t s : 285714$ $w h i c h i s r e p e a t e d i n d e f i n i t e d .$ $d e t e r m i n a t e t h e f r a c t i o n \frac{a}{b}$
Commented by mr W last updated on 18/Nov/20

$0.285714 . . . = x$ $285714 + x = 100000 x$ $285714 = 999999 x$ $x = \frac{285714}{999999} = \frac{2}{7} = \frac{a}{b}$
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

	$l e t p = 0.285714285714 . . .$ $\Rightarrow 1000000 p = 285714.285714 . . .$ $s u b t r a c t (2) b y (1)$ $999999 p = 285714 \Rightarrow p = \frac{285714}{999999} = \frac{2}{7}$
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