Question

The value of the decimal $3.23\overline{574}$ in fraction is equal to

• A. $\frac{323251}{99900}$
• B. $\frac{323574}{100000}$
• C. $\frac{323574}{99999}$
• D. $\frac{323251}{99999}$

Answer 1

The correct option is A $\frac{323251}{99900}$

Let $x=3.23\overline{574}$
$\Rightarrow 100x=323.\overline{574}...\left(1\right)$
$\Rightarrow 100000x=323574.\overline{574}...\left(2\right)$
Subtracting eqn $\left(1\right)$ from $\left(2\right)$
$100000x-100x=323574.\overline{574}-323.\overline{574}$
$\Rightarrow 99900x=323251$
$\Rightarrow x=\frac{323251}{99900}$

Alternate Solution:
$3.23\overline{574}=\frac{323574-323}{100000-100}=\frac{323251}{99900}$