Question

0.47bar in the form of p/q

Answer 1

I hope it will help you.

Answer 2

Let 0.$\overline{47} = x$     ...( i )

As there two numbers under bar, to make them out of the decimal multiply by 100 ( number of zeroes is dependent on the number of numbers under bar ).

∴ 100 × x = 100 × 0.$\overline{47}$

⇒ 100x = 47.$\overline{47}$    ...( ii )

Now subtract ( i ) from ( ii ),

100x = 47.$\overline{47}$

   - x = - 0.$\overline{47}$

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99 x = 47 [ bar cancel ]

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x = $\dfrac{47}{99}$

Substituting the value of x from ( i ),

0.$\overline{47} = \dfrac{47}{99}$

therefore, 0.$\overline{47}$ in the form of p/q is 47/99.