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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) \(\frac{23}{90}\)**.

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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!

Convert the repeating decimal 0.2555… to a fraction.

Learn how to convert the repeating decimal 0.2555… into a fraction step-by-step. This tutorial covers algebraic manipulation to isolate the repeating part and simplifies the decimal to the fraction 23/90. Ideal for students in Grades 8-10.

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