Question
Write the following rational numbers in $\frac{p}{q}$ form. : $\quad 0 . \overline{37}$
✓
Answer
Let $x=0 . \overline{37}$
$\therefore x = 0.3737…$
Since, two numbers i.e. $3$ and $7$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x = 37.3737……$
$\therefore 100 x =37 . \overline{37} \ldots \ldots \text {..(ii) }$
Subtracting (i) from (ii),
$100 x-x=37 . \overline{37}-0 . \overline{37}$
$\therefore 99x = 37$
$\therefore \quad x=\frac{37}{99}$
$\therefore \quad 0 . \overline{37}=\frac{37}{99}$
$\therefore x = 0.3737…$
Since, two numbers i.e. $3$ and $7$ are repeating after the decimal point.
Thus, multiplying both sides by $100,$
$100x = 37.3737……$
$\therefore 100 x =37 . \overline{37} \ldots \ldots \text {..(ii) }$
Subtracting (i) from (ii),
$100 x-x=37 . \overline{37}-0 . \overline{37}$
$\therefore 99x = 37$
$\therefore \quad x=\frac{37}{99}$
$\therefore \quad 0 . \overline{37}=\frac{37}{99}$
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