convert 9.999---- = 9.9- in p/q form

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Solution

$D e a r s t u d e n t, L e t x = 9.99999 . . . . . . . . . . . . (1) \Rightarrow x = 9 . \bar{9} . . . . (2) m u l t i p l y e q n (1) b y 10 10 x = 99.99999999 . . . . . . 10 x = 99 . \bar{9} . . . (3) S u b t r a c t e q n (2) f r o m e q n (3) 10 x - x = 99 . \bar{9} - 9 . \bar{9} 9 x = 91 x = 9.99999 . . . . . . . . = \frac{91}{9} R e g a r d s$

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