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Ex 1.3,2 - You know that 1/7 = 0.(142857) = 0.142857142857 - Finding decimal expansion

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Ex1.3, 2 You know that 1/7 = 0.(142857) ̅ = 0.142857142857…. . Can you predict what the decimal expansion 2/7 , 3/7 , 4/7 , 5/7 ,6/7 of are, without actually doing the long division? If so, how? [Hint: Study the remainders while finding the value of 1/7 carefully.] Thus, 1/7 = 0.(142857) ̅ 2/7 = 0.(285714) ̅ 3/7 = 0.(428571) ̅ 4/7 = 0.(571428) ̅ 5/7 = 0.(714285) ̅ & 6/7 = 0.(857142) ̅ .

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.