Express 0.121212... as a fraction.
\(\dfrac{4}{33}\)
Step 1 – set up the recurring decimal as a variable. Let:
\(x = 0.\overline{12} = 0.121212\ldots\)
Step 2 – multiply by 100 (since the repeating block has 2 digits):
\(100x = 12.121212\ldots\)
Step 3 – subtract:
\(100x - x = 12.121212\ldots - 0.121212\ldots\)
\(99x = 12 \implies x = \dfrac{12}{99} = \dfrac{4}{33}\)
Hence, \(0.\overline{12} = \dfrac{4}{33}\).
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