Question

Find the fraction form of the decimal 0.12121212....... .

• A. $\frac{4}{3}$
• B. $\frac{12}{100}$
• C. $\frac{4}{99}$
• D. $\frac{4}{33}$

Answer 1

The correct option is D $\frac{4}{33}$

Let '$x$' be 0.1212121212....
In this decimal, the digits 12 gets repeated. So multilpy $x$ with 100.
$\Rightarrow$ 100$x$ = 12.12121212....
= 12 + 0.121212.....
= 12 + $x$ $(\because x=\mathrm{0.121212....})$
$\Rightarrow$ 99$x$ = 12
$\Rightarrow$ $x$ = $\frac{12}{99}$
= $\frac{4}{33}$
$\therefore$ Fraction form of the decimal 0.12121212....... is $\frac{4}{33}.$