Question

The fraction form of decimal 0.636363..... is ____

• A. $\frac{3}{63}$
• B. $\frac{7}{33}$
• C. $\frac{63}{100}$
• D. None of the above

Answer 1

The correct option is B $\frac{7}{33}$

Let '$x$' be 0.636363....
In this decimal, the digits 63 gets repeated. So multilpy $x$ with 100.
$\Rightarrow$ 100$x$ = 63.636363....
= 63 + 0.636363.....
= 63 + $x$ $(\because x=\mathrm{0.636363....})$
$\Rightarrow$ 99$x$ = 63
$\Rightarrow$ $x$ = $\frac{63}{99}$
= $\frac{7}{11}$
$\therefore$ Fraction form of the decimal 0.636363....... is $\frac{7}{11}$