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Convert 0.575757.. to p/q form where p and q are integers and q ≠ 0
Last updated at March 22, 2023 by Teachoo
Expressing decimal in p/q
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Convert 0.575757.. to p/q form where p and q are integers and q ≠ 0 You are here
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Expressing numbers in p/q form
Example 6
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Example 8
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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.(57) ̅ to p/q form where p and q are integers and q ≠ 0 Let x = 0.57575757….. Multiplying equation (1) with 100 100x = 100 × (0.57575757…) 100x = 57.575757… Subtracting (2) from (1) i.e. (2) – (1) 100x – x = 57.575757… – 0.575757… 99x = 57 Since there is bar over 5 and 7, (two digits) x = 𝟓𝟕/𝟗𝟗 Thus, 0.(57) ̅ = 𝟓𝟕/𝟗𝟗
