Question

50 points plss express as p and q 1.314 ( bar on 314)

Answer 1

X = 1.314314314.. i) equation.

peridiocity = 3

Multiply 1000 on both sides of the equation.

1000X =1314.314314.... ii) equation.

Subtract equation i) from ii).

1000X = 1314.314314
- X = 1.314314

999X= 1313.000000

999X= 1313

X = 1313/999.

Answer 2

$\text{Let } x = 1.\overline{314}$
$\text{or, } x = 1.314314314314... \,\,\, ...(i)$
$\therefore 10x = 13.14314314314...$
$\therefore 100x = 131.4314314314...$
$\therefore 1000x = 1314.314314314... \,\,\, ...(ii)$
$\text{Substracting eq.(i) from eq.(ii) ...}$
$1000x-x = 1314.\overline{314} - 1.\overline{314}$
$999x = 1313$
$x = \displaystyle\frac{1313}{999}$

$\therefore \,\,\,\,^{p}/_{q} \text{ of } 1.\overline{314} \text{ is } \displaystyle \frac{1313}{999}$