Question

You know that `1/7=0.bar142857.` Can you predict what the decimal expansions 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.]

Answer 1

Yes, it can be done as follows

`2/7=2xx1/7=2xx0.bar142857=0.bar285714`

`3/7=3xx1/7=3xx0.bar142857=0.bar428571`

`4/7=4xx1/7=4xx0.bar142857=0.bar571428`

`5/7=5xx1/7=5xx0.bar142857=0.bar714285`

`6/7=6xx1/7=6xx0.bar142857=0.bar857142`