Express each of the following as a recurring decimal :
`3/11`

Answer

To express the fraction \( \frac{3}{11} \) as a recurring decimal, we will perform long division. Here are the steps:

### Step-by-Step Solution:

1. **Set Up the Division**: We want to divide 3 by 11. Since 3 is less than 11, we start with 0.

\[ 3 \div 11 = 0. \]

2. **Add Decimal Point**: We add a decimal point and a zero to 3, making it 30.

\[ 3.0 \div 11. \]

3. **Divide**: Now, we see how many times 11 goes into 30. It goes 2 times (since \( 11 \times 2 = 22 \)).

\[ 30 - 22 = 8. \]

4. **Bring Down Another Zero**: We now bring down another 0, making it 80.

\[ 80 \div 11. \]

5. **Divide Again**: 11 goes into 80 a total of 7 times (since \( 11 \times 7 = 77 \)).

\[ 80 - 77 = 3. \]

6. **Repeat the Process**: Now, we bring down another 0, making it 30 again. We notice that we are back to where we started.

\[ 30 \div 11 \text{ (which we already calculated)}. \]

7. **Identify the Recurring Part**: The division will continue to repeat the sequence of 2 and 7. Therefore, we can express \( \frac{3}{11} \) as:

\[ 0.272727... \]

8. **Use Bar Notation**: To indicate that 27 is the recurring part, we write it as:

\[ 0.\overline{27}. \]

### Final Answer:
Thus, \( \frac{3}{11} \) can be expressed as the recurring decimal \( 0.\overline{27} \).

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