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Ex1.3, 3 Express the following in the form 𝑃/𝑞 where p and q are integers and q ≠ 0. (iii) 0. (001) ̅ Let x = 0.(001) ̅ = 0.001001… Multiplying equation (1) with 1000 1000x = 1000 × (0.001001…) 1000x = 1.001001… Subtracting (2) from (1) i.e. (2) – (1) 1000x – x = 1.001001… – 0.001001… 999x = 1 x = 1/999 x = 1/999 Thus, 0.(001) ̅ = 1/999

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.