Question

Express the number 0.3178(bar on 178) in the form of rational number p/q

Answer 1

$z=\mathrm{0.3178178178178....}$

$10z=\mathrm{3.178178178178.....}$ (1)

$10000z=\mathrm{3178.178178178....}$ (2)

(2)-(1), we get

$9990z=3175$

$\Rightarrow z=\frac{3175}{9990}$

$\Rightarrow z=\frac{635}{1998}$