Question

1
6. You know that
= 0.142857. Can you predict what
7
2 3 4 5 6
the decimal expansions of
7'7' 7'7'7 are
without actually doing the long division ? If so, how?
[Hint : Study the remaniders while finding the
1
value of carefully.]​

Answer 1

Answer:

Yes, we can predict the decimal expansion without actually doing long division.

A.T.Q

1/7= 0. 142857 ( given)

2/7= 2 × 1/7 = 0.285714

3/7 = 3× 1/7 = 0.428571

4/7 = 4× 1/7= 0.571428

5/7 = 5× 1/7= 0. 714285

6/7 = 6× 1/7 = 0. 857142

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Hope this will help you....