[tex]0.(4) = \frac{4}{9} [/tex]
[tex]0.(54) = \frac{54}{99} = \frac{18}{33} = \frac{6}{11} [/tex]
[tex]0.(940) = \frac{940}{999} [/tex]
[tex]0.3(4) = \frac{34 - 3}{90} = \frac{31}{90} [/tex]
[tex]0.45(5) = \frac{455 - 45}{900} = \frac{410}{900} = \frac{41}{90} [/tex]
[tex]0.253(9) = \frac{2539 - 253}{9000} = \frac{2286}{9000} = \frac{762}{3000} = \frac{254}{1000} = \frac{127}{500} [/tex]