By actural division , express each of the following as a repeating decimal :
`7/12`

Answer

To express \( \frac{7}{12} \) as a repeating decimal using actual division, follow these steps:

### Step 1: Set up the division
We start by dividing 7 by 12. Since 7 is less than 12, we add a decimal point and a zero to 7, making it 7.0.

### Step 2: Perform the division
1. **Divide 70 by 12**:
- 12 goes into 70 five times (since \( 12 \times 5 = 60 \)).
- Write down 5 after the decimal point.
- Subtract 60 from 70, which gives us a remainder of 10.

2. **Bring down the next zero**:
- Now we have 10.
- Add another zero making it 100.

3. **Divide 100 by 12**:
- 12 goes into 100 eight times (since \( 12 \times 8 = 96 \)).
- Write down 8 after the 5, making it 0.58.
- Subtract 96 from 100, which gives us a remainder of 4.

4. **Bring down the next zero**:
- Now we have 40.

5. **Divide 40 by 12**:
- 12 goes into 40 three times (since \( 12 \times 3 = 36 \)).
- Write down 3 after the 8, making it 0.583.
- Subtract 36 from 40, which gives us a remainder of 4.

### Step 3: Notice the repeating pattern
Now we see that we have a remainder of 4 again, which means the next steps will repeat the division of 40 by 12, yielding another 3.

Thus, we can conclude that the decimal will continue with 3 repeating indefinitely.

### Final Answer
Therefore, \( \frac{7}{12} = 0.58\overline{3} \) (where the bar indicates that the 3 repeats).

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