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2. You know that \(1/7 = 0\overline{.142857.}\) 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 1/7 of carefully.]
Answer :

We have, \(1/7 = 0\overline{.142857}\)
2/7 = 2 × 1/7
\(= 2 × 0\overline{.142857}\)
i.e. \(2/7 = 0\overline{.285714}\)

3/7 = 3 × 1/7
\(= 3 × 0\overline{.142857}\)
i.e. \(3/7 = 0\overline{.428571}\)

4/7 = 4 × 1/7
\(= 4 × 0\overline{.142857}\)
i.e. \(4/7 = 0\overline{.571428}\)

5/7 = 5 × 1/7
\(= 5 × 0\overline{.142857}\)
i.e. \(5/7 = 0\overline{.714285}\)

6/7 = 6 × 1/7
\(= 6 ×0 \overline{.142857}\)
i.e. \(6/7 = 0\overline{.857142}\)