Question

Write a rational number for 8.555…..

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{8.55555.........}$

$\underline{\textsf{To find:}}$

$\textsf{Rational form of the given number}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\text{Let}\;\mathsf{x=8.5555........}$........(1)

$\implies\mathsf{10x=85.5555.......}$.......(2)

$\textsf{Subtracting (1) from (2) we get}$

$\mathsf{10x-x=77}$

$\mathsf{9x=77}$

$\implies\boxed{\mathsf{x=\dfrac{77}{9}}}$

$\underline{\textsf{Answer:}}$

$\mathsf{8.5555.......=\dfrac{77}{9}}$

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