Question

The value of the decimal $1.\overline{43}$ is equal to

• A. $\frac{143}{100}$
• B. $\frac{144}{101}$
• C. $\frac{143}{99}$
• D. $\frac{142}{99}$

Answer 1

The correct option is D $\frac{142}{99}$

Let $x=1.\overline{43}$
$\Rightarrow 100x=143.\overline{43}$
$\Rightarrow 100x-x=143.\overline{43}-1.\overline{43}$
$\Rightarrow 99x=142$
$\Rightarrow x=\frac{142}{99}$

Alternate Solution:
$1.\overline{43}=\frac{143-1}{100-1}=\frac{142}{99}$