To solve \( 1.8\overline{3} \), we represent this repeating decimal as a fraction.

Let:
\[
x = 1.8\overline{3}
\]
This means \( x = 1.83333\ldots \) where the digit 3 repeats infinitely.

### Step 1: Multiply by 10 to shift the decimal point:
\[
10x = 18.83333\ldots
\]

### Step 2: Subtract the original equation from this new equation:
\[
10x - x = 18.83333\ldots - 1.83333\ldots
\]
\[
9x = 17
\]

### Step 3: Solve for \( x \):
\[
x = \frac{17}{9}
\]

Thus, \( 1.8\overline{3} = \frac{17}{9} \).

Would you like more details or have any questions?

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Here are five related questions:
1. How do you convert repeating decimals into fractions?
2. What is the decimal form of \( \frac{17}{9} \)?
3. Can all repeating decimals be expressed as fractions?
4. How do non-repeating decimals differ in conversion to fractions?
5. What happens when the repeating part includes more than one digit?

**Tip:** A repeating decimal can always be expressed as a fraction, where the repeating part helps determine the denominator!

Learn how to convert the repeating decimal 1.8\overline{3} into a fraction. This detailed solution explains each step, including key algebraic techniques and concepts. Perfect for students in Grades 8-10.

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