Example 9 - Chapter 1 Class 9 Number Systems
Last updated at July 15, 2026 by Teachoo
Expressing decimal in p/q
Convert 2.333... to p/q form where p and q are integers and q ≠ 0
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Chapter 1 Class 9 Number Systems
Concept wise
- Rational numbers - Definition
- Finding rational number between two numbers
- Irrational Numbers
- Simplifying real numbers
- Rationalising
- Laws of exponents
- Finding decimal expansion
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Expressing decimal in p/q
- Classifiying rational/irrational
- Finding irrational numbers b/w two numbers
- Real numbers on a number line
Transcript
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
