By actural division , express each of the following as a repeating decimal :
`212/143`

Answer

To express \( \frac{212}{143} \) as a repeating decimal using actual division, we will follow these steps:

### Step 1: Set up the division
We will divide 212 by 143.

### Step 2: Perform the division
1. **Divide 212 by 143**:
- 143 goes into 212 once (1).
- So, \( 1 \times 143 = 143 \).
- Subtract: \( 212 - 143 = 69 \).

2. **Bring down a decimal**:
- Since 69 is less than 143, we add a decimal point and a zero to make it 690.

3. **Divide 690 by 143**:
- 143 goes into 690 four times (4).
- So, \( 4 \times 143 = 572 \).
- Subtract: \( 690 - 572 = 118 \).

4. **Bring down another zero**:
- Now we have 1180.

5. **Divide 1180 by 143**:
- 143 goes into 1180 eight times (8).
- So, \( 8 \times 143 = 1144 \).
- Subtract: \( 1180 - 1144 = 36 \).

6. **Bring down another zero**:
- Now we have 360.

7. **Divide 360 by 143**:
- 143 goes into 360 two times (2).
- So, \( 2 \times 143 = 286 \).
- Subtract: \( 360 - 286 = 74 \).

8. **Bring down another zero**:
- Now we have 740.

9. **Divide 740 by 143**:
- 143 goes into 740 five times (5).
- So, \( 5 \times 143 = 715 \).
- Subtract: \( 740 - 715 = 25 \).

10. **Bring down another zero**:
- Now we have 250.

11. **Divide 250 by 143**:
- 143 goes into 250 once (1).
- So, \( 1 \times 143 = 143 \).
- Subtract: \( 250 - 143 = 107 \).

12. **Bring down another zero**:
- Now we have 1070.

13. **Divide 1070 by 143**:
- 143 goes into 1070 seven times (7).
- So, \( 7 \times 143 = 1001 \).
- Subtract: \( 1070 - 1001 = 69 \).

### Step 3: Identify the repeating part
At this point, we notice that we have returned to the remainder of 69, which we had earlier. This indicates that the decimal will start repeating from here.

### Final Result
The result of \( \frac{212}{143} \) expressed as a repeating decimal is:
\[ 1.482517\overline{482517} \]