The decimal \( 2.\overline{3} \) (2.3 repeated) can be converted into a fraction using the following steps:

Let \( x = 2.\overline{3} \).

### Step 1: Eliminate the repeating decimal
To do this, multiply both sides by 10:
\[
10x = 23.\overline{3}
\]

### Step 2: Subtract the original equation from the new one
Subtract \( x = 2.\overline{3} \) from \( 10x = 23.\overline{3} \):
\[
10x - x = 23.\overline{3} - 2.\overline{3}
\]
\[
9x = 21
\]

### Step 3: Solve for \( x \)
\[
x = \frac{21}{9}
\]
Simplify the fraction:
\[
x = \frac{7}{3}
\]

Thus, \( 2.\overline{3} = \frac{7}{3} \).

Would you like further details or have any questions?

Here are some related questions:
1. How do you convert other repeating decimals to fractions?
2. Can all repeating decimals be expressed as fractions?
3. What is the general method for converting decimals into fractions?
4. How do you simplify a fraction?
5. How can we convert a mixed repeating decimal (like 1.45\(\overline{6}\)) into a fraction?

**Tip**: For any repeating decimal, multiplying by a power of 10 is the key to eliminating the repeating part for easier conversion to fractions.

Learn how to convert the repeating decimal 2.3 (2.\overline{3}) into a fraction with a clear step-by-step process. This guide explains the algebraic method for handling repeating decimals and simplifying fractions. Perfect for students in Grades 6-8.

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