Example 9 - Show that 0.2353535.. = 0.235 can be expressed - Expressing decimal in p/q

  1. Chapter 1 Class 9 Number Systems
  2. Serial order wise
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Example 9 Show that 0.2353535…… = 0.2(35) ̅ can be expressed in the form 𝑝/𝑞 , where p and q are integers and q ≠ 0. Let x = 0.2(35) ̅ = 0.2353535… Multiplying equation (1) with 100 100x = 100 × (0.2353535…) 100x = 23.53535… Subtracting (2) from (1) i.e. (2) – (1) 100x – x = 23.53535… – 0.2353535… 99x = 23.3000 x = 23.3/99 x = 233/990 Thus, 0.2(35) ̅ = 233/990

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.