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You know that 1/7=0. bar 142857Can you p...

You know that `1/7=0. bar 142857`Can you predict what the decimal expansion of `2/7,3/7,4/7,5/7,6/7`are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of `1/7` carefully.]

Text Solution

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given, `1/7`=`0.overline(142857)`
`2/7`=`2xx(1/7)`=`2xx0.overline(142857)` = `2xx0.overline(285714)`
`3/7`=`3xx(1/7)`=`3xx0.overline(142857)` = `3xx0.overline(428571)`
`4/7`=`4xx(1/7)`=`4xx0.overline(142857)` = `4xx0.overline(571428)`
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