1) 0,5(3) = 0,53
$$ x = 0,5(3) $$
$$ 1000x = 53,333... $$
$$ 1000x = 53 + 0,333... $$
$$ 1000x = 53 + 0,3(3) $$
$$ 1000x = 53 + x $$
$$ 999x = 53 $$
$$ x = \frac{53}{999} = \frac{17}{319} $$
2) 0,17(8) = 0,178
$$ x = 0,17(8) $$
$$ 100x = 17,8888... $$
$$ 100x = 17 + 0,8888... $$
$$ 100x = 17 + 0,8(8) $$
$$ 100x = 17 + x $$
$$ 99x = 17 $$
$$ x = \frac{17}{99} $$
3) 0,23(16) = 0,2316
$$ x = 0,23(16) $$
$$ 100x = 23,161616... $$
$$ 100x = 23 + 0,1616(16) $$
$$ 100x = 23 + 0,16(16) $$
$$ 100x = 23 + x $$
$$ 99x = 23 $$
$$ x = \frac{23}{99} $$
4) 0,14(234) = 0,14234
$$ x = 0,14(234) $$
$$ 1000x = 142,342342... $$
$$ 1000x = 142 + 0,342(342) $$
$$ 1000x = 142 + 0,3(42) $$
$$ 1000x = 142 + x $$
$$ 999x = 142 $$
$$ x = \frac{142}{999} = \frac{142}{999} $$
1) 0,5(3) = 0,53
$$ x = 0,5(3) $$
$$ 1000x = 53,333... $$
$$ 1000x = 53 + 0,333... $$
$$ 1000x = 53 + 0,3(3) $$
$$ 1000x = 53 + x $$
$$ 999x = 53 $$
$$ x = \frac{53}{999} = \frac{17}{319} $$
2) 0,17(8) = 0,178
$$ x = 0,17(8) $$
$$ 100x = 17,8888... $$
$$ 100x = 17 + 0,8888... $$
$$ 100x = 17 + 0,8(8) $$
$$ 100x = 17 + x $$
$$ 99x = 17 $$
$$ x = \frac{17}{99} $$
3) 0,23(16) = 0,2316
$$ x = 0,23(16) $$
$$ 100x = 23,161616... $$
$$ 100x = 23 + 0,1616(16) $$
$$ 100x = 23 + 0,16(16) $$
$$ 100x = 23 + x $$
$$ 99x = 23 $$
$$ x = \frac{23}{99} $$
4) 0,14(234) = 0,14234
$$ x = 0,14(234) $$
$$ 1000x = 142,342342... $$
$$ 1000x = 142 + 0,342(342) $$
$$ 1000x = 142 + 0,3(42) $$
$$ 1000x = 142 + x $$
$$ 999x = 142 $$
$$ x = \frac{142}{999} = \frac{142}{999} $$