By actural division , express each of the following as a repeating decimal :
`227/30`

Answer

To express \( \frac{227}{30} \) as a repeating decimal using actual division, we will follow these steps:

### Step-by-Step Solution:

1. **Set up the division**: We need to divide 227 by 30. We can write this as \( 227 \div 30 \).

2. **Perform the division**:
- **First Division**: 30 goes into 227. We find how many times 30 fits into 227.
- \( 30 \times 7 = 210 \) (since \( 30 \times 8 = 240 \) which is too high).
- Write down 7 as the whole number part of the quotient.
- Subtract \( 210 \) from \( 227 \):
\[ 227 - 210 = 17 \]

3. **Add decimal point**: Since we have a remainder, we add a decimal point and a zero to the remainder (17 becomes 170).

4. **Continue the division**:
- **Next Division**: Now we divide 170 by 30.
- \( 30 \times 5 = 150 \)
- Write down 5 in the decimal part of the quotient.
- Subtract \( 150 \) from \( 170 \):
\[ 170 - 150 = 20 \]

5. **Add another zero**: Add a zero to the remainder (20 becomes 200).

6. **Continue the division**:
- **Next Division**: Now divide 200 by 30.
- \( 30 \times 6 = 180 \)
- Write down 6 in the decimal part of the quotient.
- Subtract \( 180 \) from \( 200 \):
\[ 200 - 180 = 20 \]

7. **Repeat the process**: Notice that we are back to a remainder of 20, which we already encountered. This means the decimal will repeat.
- Add a zero to 20 (20 becomes 200) and repeat the division.
- Each time, we will get 6, leading to the repeating decimal.

8. **Final result**: The quotient can be expressed as:
\[ 7.56666\ldots \]
This can be written as \( 7.5\overline{6} \) where \( 6 \) is the repeating part.

### Final Answer:
Thus, \( \frac{227}{30} \) can be expressed as \( 7.5\overline{6} \).