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The problem asks to convert the repeating decimal \(0.\overline{93}\) into a fraction.

Let's solve this step by step:

### Step 1: Set up the repeating decimal
Let \( x = 0.\overline{93} \) which means:
\[
x = 0.93939393\ldots
\]

### Step 2: Eliminate the repeating part
To eliminate the repeating decimal, multiply both sides of the equation by 100 (since the repeating part consists of two digits):
\[
100x = 93.93939393\ldots
\]

### Step 3: Subtract the two equations
Now subtract the original equation \(x = 0.\overline{93}\) from \(100x = 93.\overline{93}\):
\[
100x - x = 93.93939393\ldots - 0.93939393\ldots
\]
\[
99x = 93
\]

### Step 4: Solve for \(x\)
Now, divide both sides by 99:
\[
x = \frac{93}{99}
\]

### Step 5: Simplify the fraction
The greatest common divisor (GCD) of 93 and 99 is 3. So divide both the numerator and the denominator by 3:
\[
x = \frac{93 \div 3}{99 \div 3} = \frac{31}{33}
\]

Thus, \(0.\overline{93} = \frac{31}{33}\).

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Convert \( 0.\overline{72} \) into a fraction.
2. Express \( 0.\overline{47} \) as a fraction in simplest form.
3. How would you convert \( 0.\overline{123} \) to a fraction?
4. What is the fractional equivalent of \( 0.\overline{58} \)?
5. Simplify \( 0.\overline{19} \) as a fraction.

**Tip:** For repeating decimals, the number of digits in the repeating sequence determines how many powers of 10 to multiply by.

Convert the following repeating decimal to a fraction: 0.93̅

Learn how to convert the repeating decimal 0.93̅ into a fraction using algebraic methods. This step-by-step solution simplifies the decimal to the fraction 31/33 by applying GCD. Suitable for Grades 7-10.

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