Question

0.09bar to show in the form of p/q ​

Answer 1

${\huge{\underline{\green {\sf{Answer}}}}}$

Here , we have to show the given value in the form of $\dfrac {p}{q}$

For this,

➫Let x = $0.0\overline{9}$...................... (i)

On multiplying equation (i) by 10

➫10x = $0.\overline{9}$

➫10x =$0.999.......... (ii)$

On multiplying equation (ii) by 10

➫100x = 9.999............ (iii)

Now, (iii) - (ii)

➫100x = 9.999.......... (-) 10x = 0.999..........

➫90x = 9.000..........

➫x = $\dfrac{9}{90}$

➫ x = $\dfrac{1}{10}$

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