The decimal \( 3.28\overline{28} \) (where "28" repeats indefinitely) can be expressed as a fraction by following these steps:

### Step 1: Define the repeating decimal.
Let:
\[
x = 3.28\overline{28}
\]

### Step 2: Isolate the repeating part.
To isolate the repeating part, multiply the equation by 100 (since the repeating block "28" is two digits long):
\[
100x = 328.28\overline{28}
\]

### Step 3: Subtract the original equation from the new one.
Now subtract the original equation \( x = 3.28\overline{28} \) from \( 100x = 328.28\overline{28} \):
\[
100x - x = 328.28\overline{28} - 3.28\overline{28}
\]
\[
99x = 325
\]

### Step 4: Solve for \( x \).
Now, solve for \( x \) by dividing both sides by 99:
\[
x = \frac{325}{99}
\]

### Step 5: Simplify the fraction (if possible).
The fraction \( \frac{325}{99} \) is already in its simplest form, so:
\[
3.28\overline{28} = \frac{325}{99}
\]

Thus, \( 3.28\overline{28} \) as a fraction is \( \frac{325}{99} \).

Would you like more details or have any questions about the steps?

Here are 5 related questions:
1. How do you convert other repeating decimals to fractions?
2. How can you simplify complex fractions?
3. What are the properties of repeating decimals?
4. What is the difference between terminating and repeating decimals?
5. How do you multiply or divide fractions with repeating decimals?

**Tip:** When working with repeating decimals, multiplying by powers of 10 that match the length of the repeating block helps eliminate the repeating part.

Learn how to convert the repeating decimal 3.28 (where '28' repeats indefinitely) into a fraction. This step-by-step solution involves isolating the repeating part, subtracting equations, and simplifying the result. Suitable for students in Grades 8-10.

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