By actural division , express each of the following as a repeating decimal :
`303/11`

Answer

To express \( \frac{303}{11} \) as a repeating decimal through actual division, we will follow these steps:

### Step 1: Set Up the Division
We will divide 303 by 11.

### Step 2: Divide the Whole Number
1. **Divide 303 by 11**:
- 11 goes into 30 two times (since \( 11 \times 2 = 22 \)).
- Write down 2 above the line.
- Subtract \( 22 \) from \( 30 \) to get \( 8 \).
- Bring down the next digit (3) to make it \( 83 \).

### Step 3: Continue Dividing
2. **Divide 83 by 11**:
- 11 goes into 83 seven times (since \( 11 \times 7 = 77 \)).
- Write down 7 above the line next to 2.
- Subtract \( 77 \) from \( 83 \) to get \( 6 \).

### Step 4: Introduce Decimal Point
3. **Add Decimal Point**:
- Since we have a remainder, we will add a decimal point and a zero to the remainder (making it \( 60 \)).
- Now we are dividing \( 60 \) by \( 11 \).

### Step 5: Continue Dividing with Decimal
4. **Divide 60 by 11**:
- 11 goes into 60 five times (since \( 11 \times 5 = 55 \)).
- Write down 5 above the line next to 27.
- Subtract \( 55 \) from \( 60 \) to get \( 5 \).

### Step 6: Repeat the Process
5. **Bring Down Another Zero**:
- Add another zero to the remainder (making it \( 50 \)).
- Now divide \( 50 \) by \( 11 \).

6. **Divide 50 by 11**:
- 11 goes into 50 four times (since \( 11 \times 4 = 44 \)).
- Write down 4 above the line next to 275.
- Subtract \( 44 \) from \( 50 \) to get \( 6 \) again.

### Step 7: Identify the Repeating Pattern
7. **Recognize the Repeating Decimal**:
- We notice that we are back to dividing \( 60 \) again, which will repeat the previous steps.
- Therefore, the decimal part \( 54 \) will keep repeating.

### Final Result
Putting it all together, we find:
\[ \frac{303}{11} = 27.545454\ldots \]
Thus, we can express this as:
\[ 27.\overline{54} \]