Ex 1.5, 3 - Recall, pi is defined as ratio of circumference - Classifiying rational/irrational

  1. Chapter 1 Class 9 Number Systems
  2. Serial order wise
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Ex1.5, 3 Recall, Ο€ is defined as the ratio of the circumference (sayΒ c) of a circle to its diameter (sayΒ d). That is,Β πœ‹ = 𝑐/𝑑 . This seems to contradict the fact that Ο€ is irrational. How will you resolve this contradiction? Ο€ = 𝑐/𝑑 is a rational number when c & d both are rational numbers But the c & d we calculate is not exactly a rational number and either c or d or both can be irrational numbers, Since, π‘…π‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™/πΌπ‘Ÿπ‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘›π‘Žπ‘™ = Irrational So, Ο€ is irrational.

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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.