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Show that 0.142857142857…..=1/7....

Show that 0.142857142857…..`=1/7`.

Text Solution

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Let x=0.142857142857……..
On multiplying both sides of Eq . (i) by 100000, we get
10000000x=142857.142857……
On subtracting Eq. (i) from Eq. (ii). We get
1000000 x-x = ( 142857.142857…..)- (0.142857….)
999999x-142857
`x(142857)/(999999)=1/7`
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