Question

$0.\overline{423}$ equals

• A. $\frac{419}{990}$
• B. $\frac{419}{999}$
• C. $\frac{417}{990}$
• D. $\frac{423}{999}$

Answer 1

The correct option is D

$\frac{423}{999}$

Explanation for correct options:

Let, $x=0.\overline{423}$

$\Rightarrow 1000x=423.\stackrel{\rightharpoonup }{423}$

$\Rightarrow 999x+x=423.\stackrel{\rightharpoonup }{423}$

$\Rightarrow 999x=423.\stackrel{\rightharpoonup }{423}-x$

$\Rightarrow 999x=423.\stackrel{\rightharpoonup }{423}-0.\stackrel{\rightharpoonup }{423}$

$\Rightarrow 999x=423$

$\Rightarrow x=\frac{423}{999}$

Therefore, $0.\overline{423}$ equals $\frac{423}{999}$.

Hence, Option (D) is correct.

Explanation for incorrect options:

Option (A): $\frac{419}{990}$

Since, $0.\overline{423}$ equals $\frac{423}{999}$

Therefore, $0.\overline{423}$ is not equal to $\frac{419}{990}$

Hence, Option (A) is incorrect.

Option (B): $\frac{419}{999}$

Since, $0.\overline{423}$ equals $\frac{423}{999}$

Therefore, $0.\overline{423}$ is not equal to $\frac{419}{999}$

Hence, Option (B) is incorrect.

Option (C): $\frac{417}{990}$

Since, $0.\overline{423}$ equals $\frac{423}{999}$

Therefore, $0.\overline{423}$ is not equal to $\frac{417}{990}$

Hence, Option (C) is incorrect.

Hence Option (D) is the correct .