To solve \( \frac{1}{11} \) as a decimal, here's the step-by-step division process:

### Step 1: Set up the division
We are dividing 1 by 11, so:

\[
1 \div 11
\]

### Step 2: Add decimal points and zeroes
Since 1 is smaller than 11, we start by adding a decimal point to 1, making it 1.000000 (adding zeroes as needed). 

So now we're dividing 1.000000 by 11.

### Step 3: Perform long division

1. **11 into 1:** It goes 0 times.
   \[
   0.
   \]

2. **11 into 10:** It goes 0 times again.
   \[
   0.0
   \]

3. **11 into 100:** It goes 9 times (since \( 11 \times 9 = 99 \)). Write down 9, and subtract 99 from 100, leaving a remainder of 1.
   \[
   0.09
   \]

4. **11 into 10 (bring down the next 0):** It goes 0 times again. 
   \[
   0.090
   \]

5. **11 into 100 (bring down another 0):** It goes 9 times again (since \( 11 \times 9 = 99 \)). Subtract 99 from 100, leaving a remainder of 1 again. 
   \[
   0.0909
   \]

This pattern will repeat indefinitely, so:

\[
\frac{1}{11} = 0.0909090909\ldots = 0.\overline{09}
\]

Thus, the decimal form of \( \frac{1}{11} \) is a repeating decimal \( 0.\overline{09} \).

---

Would you like further details on how repeating decimals work, or do you have any other questions?

### Related questions:
1. How do you convert repeating decimals to fractions?
2. What is the decimal representation of \( \frac{1}{7} \)?
3. How can long division help with more complex fractions?
4. Why do some fractions have repeating decimal expansions?
5. What is the relationship between fractions and decimals?

**Tip:** Always double-check your remainder when performing long division to ensure accurate results!

Learn how to solve the fraction 1/11 using long division with a detailed step-by-step solution. This problem covers essential concepts like fractions, repeating decimals, and long division, suitable for students in Grades 5-7.

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