Write 0.454545… as a fraction in lowest terms.

Step 1. Part (a). $100x = 45.4545\ldots$, so $99x = 45$ and $x = \dfrac{45}{99} = \dfrac{5}{11}$.

Step 2. Part (b), two copies. Let $y = 1.2333\ldots$. Then $100y = 123.333\ldots$ and $10y = 12.333\ldots$.

Step 3. Subtract. $90y = 111$, so $y = \dfrac{111}{90} = \dfrac{37}{30}$.