Question
Write the following rational numbers in $\frac{p}{q}$ form. : $15 . \overline{89}$
✓
Answer
Let $x=15 . \overline{89} \ldots \ldots (i)$
$\therefore x = 15.8989…$
Since, two numbers i.e. $8$ and $9$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x= 1589.8989…$
$\therefore 100 x =1589 . \overline{89} \ldots \text {.(ii) }$
$\text { Subtracting (i) from (ii), }$
$100 x - x =1589 . \overline{89}-15 . \overline{89}$
$\therefore 99 x =1574$
$\therefore \quad x=\frac{1574}{99}$
$\therefore \quad 15 . \overline{89}=\frac{1574}{99}$
$\therefore x = 15.8989…$
Since, two numbers i.e. $8$ and $9$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x= 1589.8989…$
$\therefore 100 x =1589 . \overline{89} \ldots \text {.(ii) }$
$\text { Subtracting (i) from (ii), }$
$100 x - x =1589 . \overline{89}-15 . \overline{89}$
$\therefore 99 x =1574$
$\therefore \quad x=\frac{1574}{99}$
$\therefore \quad 15 . \overline{89}=\frac{1574}{99}$
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