The given decimal in the problem is $0.2555\overline{5}$, which is a repeating decimal with the digits 5 repeating after the decimal point.

Steps to convert $0.2555\overline{5}$ to a fraction:

Let $x = 0.2555\overline{5}$.

Step 1: Isolate the repeating part

We can separate the non-repeating part (0.25) and the repeating part (the repeating 5).

Let’s multiply both sides by 10 to move one decimal place:

$10x = 2.5555\overline{5}$

Now subtract the original equation ($x = 0.2555\overline{5}$) from this new equation:

$10x - x = 2.5555\overline{5} - 0.2555\overline{5}$

$9x = 2.3$

Step 2: Solve for $x$

$x = \frac{2.3}{9} = \frac{23}{90}$

So, the fraction representation of $0.2555\overline{5}$ is:

$\boxed{\frac{23}{90}}$

Thus, the correct answer is (A) $\frac{23}{90}$.

Would you like a detailed explanation or have any questions? Here are 5 related questions you can explore:

1. How do you convert other repeating decimals to fractions?
2. Can you simplify any repeating decimals that have a non-repeating part, like 0.1234$\overline{56}$?
3. How does the process change if the repeating part starts immediately after the decimal point?
4. What is the relationship between the length of a repeating decimal and the denominator of its fractional form?
5. Can this process be used for non-repeating decimals as well?

Tip: Always check if the fractional form can be simplified by finding the greatest common divisor (GCD) between the numerator and denominator!