Question

Rewrite as a simplified fraction.

\[\large{0.\overline{2} = {?}}\]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rewrite $0.\overline{2}$ as a simplified fraction, we can call it $x$ and set up an equation, as follows:

\[x = 0.2222\ldots\]
Since the digit $2$ repeats indefinitely, we can multiply both sides of the equation by $10$ to shift the decimal point to the right:
\[10x = 2.2222\ldots\]
Now, we can subtract the original equation from the second equation and eliminate the repeating portion of the decimal:
\[10x - x = 2.2222\ldots - 0.2222\ldots\]
This simplifies to:
\[9x = 2\]
Finally, dividing both sides of the equation by $9$ gives us the value of $x$:
\[x = \dfrac{2}{9}\]
Therefore, $0.\overline{2} = \boxed{\dfrac{2}{9}}$.