Question

Express 0.121212 in the form p/q

Answer 1

$\: let \\ x = 0.121212 \: \: \: (i) \\ \\ 100x = 12.1212 \: \: \: (ii) \\ \\ substracting \: (i) \: from \: (ii) \\ \\ 100x - x = 12.1212 - 0.1212 \\ \\ 99x = 12 \\ \\ x = \frac{12}{99} \\ \\ \implies \underline{ \underline{x = \frac{4}{33} }}$