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You know that 1/7 = 0.bar(142857) can y...

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.

Text Solution

Verified by Experts

By long division, we have

`therefore (1)/(7) = 0.1428571428…. = overline(0.142857)`
Clearly, `(2)/(7) = 2xx (1)/(7) = 2xx overline0.142857 = overline0.28514,`
`(3)/(7)= 3xx(1)/(7)= 3xx overline0.14857= overline0.428571,`
`(4)/(7) = 4 xx (1)/(7) = 4xx overline0.142857 = overline0.428571,`
`(5)/(7) = 5 xx (1)/(7) = 5 xx overline0.142857= overline0.714285,`
`(6)/(7)= 6 xx (1)/(7) = 6 xx overline0.142857 = overline0.857142.`
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