Question

what is the
$\frac{p}{q}$
form of 3.131313131313

Answer 1

$\boxed{\boxed{\mathbf{\frac{310}{99}}}}$
_______________________________

Let x = $\mathsf{3. \bar{13} ----(1)}$

$\underline\text{Multiplying both sides by 100}$

[Since, the bar is on 2 digits.]

We get,

$\mathsf{100x = 313. \bar{13} ----(2)}$

$\underline\text{Subtracting equation (2)by equation (1),}$$\underline\text{ we get,}$

=> $\mathsf{(100x - x) = (313. \bar{13} - 3. \bar{13})}$

=> $\mathsf{99x = 310}$

=> $\boxed{\mathsf{x = \frac{310}{99}}}$