Convert 0.123333 .. to p/q form where p and q are integers and q ≠ 0
Last updated at Dec. 16, 2024 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
Convert 0.123 ̅ to p/q form where p and q are integers and q ≠ 0 Let x = 0.12333….. Multiplying equation (1) with 10 10x = 10 × (0.12333…) 10x = 1.23333… Subtracting (2) from (1) i.e. (2) – (1) 10x – x = 1.23333… – 0.123333… 9x = 1.11 Since there is bar over 3 only, (one digit) 1.23333… 0.12333… 9x = 111/100 x = 𝟏𝟏𝟏/𝟗𝟎𝟎 Thus, 0.123 ̅ = 𝟏𝟏𝟏/𝟗𝟎𝟎 0.123 ̅ = 𝟏𝟏𝟏/𝟗𝟎𝟎
