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Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsReal Numbers1 Mark
Question
Express the recurring decimal 7.529529529 ... in $\frac{p}{q}$ form
✓

Answer

Let $x=7.529529 \ldots=7 . \overline{529}$
$
\begin{aligned}
& \therefore \quad 1000 x=7529.529529 \ldots=7529 . \overline{529} \\
& \therefore \quad 1000 x-x=7529 . \overline{529}-7 . \overline{529} \\
& \therefore \quad 999 x=7522.0 \quad \therefore \quad x=\frac{7522}{999} \\
& \therefore \quad 7 . \overline{529}=\frac{7522}{999}
\end{aligned}
$

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