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You know that Can you predict what the decimal expansions of are, without actually doing the long division? If so how?
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Yes, we can be done this by:
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
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