Question

The value of $5.63\overline{74}-2.094\overline{26}$ is

• A. $3.543\overline{14}$
• B. $3.54314$
• C. $\frac{350778}{99900}$
• D. $\frac{350778}{99000}$

Answer 1

The correct option is D $\frac{350778}{99000}$

Let $x=5.63\overline{74}$
and $y=2.094\overline{26}$
Now, $x=5.63\overline{74}$
$\Rightarrow 100x=563.\overline{74}$
$\Rightarrow 10000x=56374.\overline{74}$
$\Rightarrow 9900x=55811$
​​​​​​​​​​​​​​$\Rightarrow x=\frac{55811}{9900}$
and $y=2.094\overline{26}$
$\Rightarrow 1000y=2094.\overline{26}$
$\Rightarrow 100000y=209426.\overline{26}$
$\Rightarrow 99000y=207332$
$\Rightarrow y=\frac{207332}{99000}$
​​​​​​​$x-y=\frac{558110}{99000}-\frac{207332}{99000}=\frac{350778}{99000}$