Express the repeating decimal 0.454545… as a fraction in its lowest terms.

The correct answer is $\frac{5}{11}$.

To express the repeating decimal 0.454545… as a fraction in its lowest terms, we can follow these steps:

Step 1: Set up an equation with a variable.
Let $x$ represent the repeating decimal:

$x=\mathrm{0.454545\dots }$

Step 2: Multiply by a power of 10.
Since there are 2 repeating digits (4 and 5), multiply both sides of the equation by 100 (10²):

$100x=\mathrm{45.454545\dots }$

Step 3: Subtract the original equation from the new equation.
Subtracting $x=\mathrm{0.454545\dots }$ from $100x=\mathrm{45.454545\dots }$:

$100x-x=\mathrm{45.454545\dots }-\mathrm{0.454545\dots }$

$99x=45$

Step 4: Solve for $x$.
Divide both sides by 99:

$x=\frac{45}{99}$

Step 5: Reduce the fraction to its lowest terms.
Divide both the numerator and denominator by their greatest common divisor, which is 9:

$x=\frac{45÷9}{99÷9}=\frac{5}{11}$

Therefore, the repeating decimal 0.454545… expressed as a fraction in lowest terms is $\frac{5}{11}$.