By actual division, express of the following rational numbers as a repeating decimal.
`5/6`

Answer

To express the rational number \( \frac{5}{6} \) as a repeating decimal through actual division, follow these steps:

### Step-by-Step Solution:

1. **Set up the division**: We need to divide 5 by 6. Since 5 is less than 6, we can start by adding a decimal point and a zero to 5, making it 5.0.

2. **Perform the division**:
- Divide 6 into 50 (the first two digits after adding the decimal).
- 6 goes into 50 a total of 8 times (since \( 6 \times 8 = 48 \)).
- Write down 8 after the decimal point.

3. **Subtract**:
- Now subtract 48 from 50, which gives us 2.
- Bring down another 0, making it 20.

4. **Continue the division**:
- Divide 6 into 20.
- 6 goes into 20 a total of 3 times (since \( 6 \times 3 = 18 \)).
- Write down 3 after the 8, making it 0.83.

5. **Subtract again**:
- Subtract 18 from 20, which gives us 2 again.
- Bring down another 0, making it 20 again.

6. **Repeat the process**:
- You will notice that dividing 6 into 20 will again give you 3, and this process will continue indefinitely.
- Thus, the decimal representation will be 0.83333..., where the digit 3 repeats.

7. **Express in repeating decimal form**:
- We can express this as \( 0.8\overline{3} \), where the bar indicates that the digit 3 repeats indefinitely.

### Final Answer:
The rational number \( \frac{5}{6} \) can be expressed as the repeating decimal \( 0.8\overline{3} \).