Question

Express:0.35 +0.28 (bar on 35 and 28)

Answer 1

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

$\mathsf{0.\overline{35}+0.\overline{28}}$

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

$\mathsf{\dfrac{p}{q}\;form\;of\;0.\overline{35}+0.\overline{28}}$

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

$\mathsf{Consider,}$

$\mathsf{0.\overline{35}+0.\overline{28}}$

$\mathsf{=0.353535\;.\;.\;.\;.+0.282828\;.\;.\;.}$

$\mathsf{=0.636363\;.\;.\;.\;.}$

$\mathsf{=0.\overline{63}}$

$\mathsf{Let\;x=0.\overline{63}}$

$\implies\mathsf{x=0.636363\;.\;.\;.}$ --------(1)

$\textsf{Multiply bothsides by 100}$

$\implies\mathsf{100\,x=63.636363\;.\;.\;.}$ --------(2)

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

$\mathsf{100\,x-x=63}$

$\implies\mathsf{99\,x=63}$

$\implies\mathsf{x=\dfrac{63}{99}}$

$\implies\mathsf{x=\dfrac{7}{11}}$

$\therefore\boxed{\mathsf{0.\overline{35}+0.\overline{28}=\dfrac{7}{11}}}$

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