Question

Find the fraction form of decimal 0.037037037....

• A. $\frac{1}{3}$
• B. $\frac{1}{27}$
• C. $\frac{1}{3}$
• D. $\frac{1}{99}$

Answer 1

The correct option is B $\frac{1}{27}$

Let '$x$' be 0.037037037....
In this decimal, the digits 037 gets repeated. So multilpy $x$ with 1000.
$\Rightarrow$ 1000$x$ = 37.037037....
= 37 + 0.037037037....
= 37 + $x$ $(\because x=\mathrm{0.037037.....})$
$\Rightarrow$ 999$x$ = 37
$\Rightarrow$ $x$ = $\frac{37}{999}$
= $\frac{1}{27}$
$\therefore$ Fraction form of the decimal 0.037037037.... is $\frac{1}{27}$.