You know that Can you predict what the decimal expansions of are, without actually doing the long division? If so how? [Hint: Study the remainders while finding the value of 1/7 carefully.]

Yes, we can do this by the following method:

2/7 = 2 * 1/7 = 2 * 0.͞1͞42͞8͞5͞7 = 0.2͞8͞5͞71͞4

3/7 = 3 * 1/7 = 3 * 0.1͞42͞8͞5͞7 = 0.4͞28͞5͞7͞1

4/7 = 4 * 1/7 = 4 * 0.1͞42͞8͞5͞7 = 0.͞57͞1͞4͞2͞8

5/7 = 5 * 1/7 = 5 * 0.1͞42͞8͞5͞7 = 0.7͞1͞4͞2͞8͞5

6/7 = 6 * 1/7 = 6 * 0.1͞42͞8͞5͞7 = 0.͞8͞5͞7͞1͞4͞2