Question

Write:
$0.6797979\dots$ can be represented in rational number as

• A. $\frac{2}{3}$
• B. $\frac{685}{1,010}$
• C. $\frac{679}{990}$
• D. $\frac{673}{990}$

Answer 1

The correct option is D $\frac{673}{990}$

Let, $m=0.6797979\dots \left(i\right)$
On multiplying both the sides by $10,$ we get
$\Rightarrow 10m=6.797979\dots \left(ii\right)$
In equations $\left(i\right)$ and $\left(ii\right)$, the digits to the right of the decimal point are not the same, so
Now, on multiplying both the sides by $100$ in $\left(i\right),$ we get
$\Rightarrow 1000m=679.797979\dots \left(iii\right)$
On subtracting equation $\left(ii\right)$ from equation$\left(iii\right)$, we get,

$\Rightarrow 990m=673\Rightarrow m=\frac{673}{990}$