Question

the decimal fraction 2.349
bar is equal to​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{2.\overline{349}}$

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

$\mathsf{\dfrac{p}{q}\;form\;of\;2.\overline{349}}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;\;x=2.\overline{349}}$

$\implies\mathsf{x=2.349\,349\,349\;.\;.\;.\;.\;.\;.}$---------(1)

$\textsf{Multiply bothsides by 1000}$

$\mathsf{1000\,x=2349.349\,349\,349\;.\;.\;.\;.\;.\;.}$---------(2)

$\mathsf{(2)-(1)\implies}$

$\mathsf{1000\,x-x=2349-2}$

$\mathsf{999\,x=2347}$

$\implies\boxed{\mathsf{x=\dfrac{2347}{999}}}$

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