By actural division , express each of the following as a repeating decimal :
`16/7`

Answer

To express \( \frac{16}{7} \) as a repeating decimal using actual division, we will follow these steps:

### Step 1: Set up the division
We need to divide 16 by 7. We write it as \( 16 \div 7 \).

### Step 2: Perform the division
- **First Division**: 7 goes into 16 two times (since \( 7 \times 2 = 14 \)).
- Write down 2 and subtract \( 14 \) from \( 16 \).
- \( 16 - 14 = 2 \).

- **Bring down a zero**: Now we have 2. We bring down a zero to make it 20.

### Step 3: Continue the division
- **Second Division**: 7 goes into 20 two times (since \( 7 \times 2 = 14 \)).
- Write down another 2 and subtract \( 14 \) from \( 20 \).
- \( 20 - 14 = 6 \).

- **Bring down a zero**: Now we have 6. We bring down a zero to make it 60.

- **Third Division**: 7 goes into 60 eight times (since \( 7 \times 8 = 56 \)).
- Write down 8 and subtract \( 56 \) from \( 60 \).
- \( 60 - 56 = 4 \).

- **Bring down a zero**: Now we have 4. We bring down a zero to make it 40.

- **Fourth Division**: 7 goes into 40 five times (since \( 7 \times 5 = 35 \)).
- Write down 5 and subtract \( 35 \) from \( 40 \).
- \( 40 - 35 = 5 \).

- **Bring down a zero**: Now we have 5. We bring down a zero to make it 50.

- **Fifth Division**: 7 goes into 50 seven times (since \( 7 \times 7 = 49 \)).
- Write down 7 and subtract \( 49 \) from \( 50 \).
- \( 50 - 49 = 1 \).

- **Bring down a zero**: Now we have 1. We bring down a zero to make it 10.

- **Sixth Division**: 7 goes into 10 one time (since \( 7 \times 1 = 7 \)).
- Write down 1 and subtract \( 7 \) from \( 10 \).
- \( 10 - 7 = 3 \).

- **Bring down a zero**: Now we have 3. We bring down a zero to make it 30.

- **Seventh Division**: 7 goes into 30 four times (since \( 7 \times 4 = 28 \)).
- Write down 4 and subtract \( 28 \) from \( 30 \).
- \( 30 - 28 = 2 \).

### Step 4: Identify the repeating part
At this point, we notice that we are back to 20, which we encountered earlier. This indicates that the digits will start repeating from here.

### Final Result
So, the decimal representation of \( \frac{16}{7} \) is:
\[ 2.285714285714... \]
We can express this as:
\[ 2.\overline{285714} \]