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Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsReal Numbers2 Marks
Question
Write the following numbers in $\frac{p}{q}$ form. : $30 . \overline{219}$
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Answer

Let $x=30 . \overline{219} \ldots$ (i)
$\therefore x =30.219219$
Since, three numbers i.e. 2, 1 and 9 are repeating after the decimal point.
Thus, multiplying both sides by 1000 ,
$1000 x =30219.219219 \ldots$
$\therefore 1000 x =30219 . \overline{219}$...(ii)
Subtracting (i) from (ii),
$1000 x-x=30219 . \overline{219}-30 . \overline{219}$
$\therefore 999 x=30189$
$\therefore \quad x=\frac{30189}{999}=\frac{3 \times 10063}{3 \times 333}$
$\therefore \quad 30 . \overline{219}=\frac{10063}{333}$

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