Question

Find the fraction form of decimal 0.123123123.....

• A. $\frac{41}{33}$
• B. $\frac{123}{1000}$
• C. $\frac{41}{333}$
• D. $\frac{12}{100}$

Answer 1

The correct option is C $\frac{41}{333}$

Let '$x$' be 0.123123....
In this decimal, the digits 123 gets repeated. So multilpy $x$ with 1000.
$\Rightarrow$ 1000$x$ = 123.123123....
= 123 + 0.123123.....
= 123 + $x$ $(\because x=\mathrm{0.123123....})$
$\Rightarrow$ 999$x$ = 123
$\Rightarrow$ $x$ = $\frac{123}{999}$
= $\frac{41}{333}$
$\therefore$ Fraction form of the decimal 0.123123....... is $\frac{41}{333}.$