Question

Rewrite as a simplified fraction.

\[\large{1.\overline{32} = {?}}\]

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rewrite the decimal $1.\overline{32}$ as a fraction, we can let $x = 1.\overline{32}$. We can then multiply both sides of this equation by 100 to eliminate the repeating decimal:

\[100x = 132.\overline{32}\]

Next, we can subtract the original equation from this new equation in order to eliminate the repeating decimal:

\[100x - x = 132.\overline{32} - 1.\overline{32}\]
\[99x = 131\]

Now, we can solve for $x$:

\[x = \frac{131}{99}\]

Thus, the simplified fraction that is equivalent to the decimal $1.\overline{32}$ is $\boxed{\frac{131}{99}}$.