Question
Write the following rational numbers in $\frac{p}{q}$ form. : $\quad 3 . \overline{17}$
✓
Answer
Letx $=3 . \overline{17}$...(i)
$\therefore x = 3.1717…$
Since, two numbers i.e. $1$ and $7$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x = 317.1717…$
$\therefore 100x= 317.17 …(ii)$
Subtracting (i) from (ii),
$100 x - x =317 . \overline{17}-3 . \overline{17}$
$\therefore 99 x =314$
$\therefore \quad x=\frac{314}{99}$
$\therefore \quad 3 . \overline{17}=\frac{314}{99} $
$\therefore x = 3.1717…$
Since, two numbers i.e. $1$ and $7$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x = 317.1717…$
$\therefore 100x= 317.17 …(ii)$
Subtracting (i) from (ii),
$100 x - x =317 . \overline{17}-3 . \overline{17}$
$\therefore 99 x =314$
$\therefore \quad x=\frac{314}{99}$
$\therefore \quad 3 . \overline{17}=\frac{314}{99} $
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