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Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsReal Numbers1 Mark
Question
Express the recurring decimal $0.777 \ldots$ in $\frac{p}{q}$ form.
✓

Answer

$
\text { Let } \begin{gathered}
x=0.777 \ldots=0 . \dot{7} \\
\therefore 10 x=7.777 \ldots=7.7 \\
\therefore \quad 10 x-x=7.7-0 . \dot{7} \\
\therefore 9 x=7 \\
\therefore x=\frac{7}{9} \\
\therefore 0.777 \ldots=\frac{7}{9}
\end{gathered}
$

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