Convert the following into a vulgar fraction :

${0.1\overline{43}}$

Let $x = 0.1\overline{43} = 0.1434343…$

Multiplying by 10 to move the decimal past the non-repeating digit:

10x = 1.434343… $\qquad$ ….. (i)

Multiplying by 1000 to move the decimal past the first repeating block:

1000x = 143.434343… $\qquad$ ….. (ii)

Subtracting (i) from (ii), we get:

$990x = 142 \\[1em] \Rightarrow x = \dfrac{142}{990} = \dfrac{71}{495}$

Hence, $0.1\overline{43} = \dfrac{71}{495}$