Express each of the following as a recurring decimal :
`22/7`

Answer

To express \( \frac{22}{7} \) as a recurring decimal, we will perform long division. Here are the steps:

### Step-by-Step Solution:

1. **Set Up the Division**: We want to divide 22 by 7. Write it as \( 22 \div 7 \).

2. **Divide**:
- 7 goes into 22 three times (since \( 7 \times 3 = 21 \)).
- Write down 3 as the whole number part of the quotient.

3. **Subtract**:
- Subtract 21 from 22, which gives us a remainder of 1.
- Write this as \( 22 - 21 = 1 \).

4. **Bring Down a Zero**:
- Since we have a remainder, we bring down a 0, making it 10.

5. **Divide Again**:
- 7 goes into 10 one time (since \( 7 \times 1 = 7 \)).
- Write down 1 in the decimal part of the quotient.

6. **Subtract Again**:
- Subtract 7 from 10, which gives us a remainder of 3.
- Write this as \( 10 - 7 = 3 \).

7. **Bring Down Another Zero**:
- Bring down another 0, making it 30.

8. **Divide Again**:
- 7 goes into 30 four times (since \( 7 \times 4 = 28 \)).
- Write down 4 in the decimal part.

9. **Subtract Again**:
- Subtract 28 from 30, which gives us a remainder of 2.
- Write this as \( 30 - 28 = 2 \).

10. **Bring Down Another Zero**:
- Bring down another 0, making it 20.

11. **Divide Again**:
- 7 goes into 20 two times (since \( 7 \times 2 = 14 \)).
- Write down 2 in the decimal part.

12. **Subtract Again**:
- Subtract 14 from 20, which gives us a remainder of 6.
- Write this as \( 20 - 14 = 6 \).

13. **Bring Down Another Zero**:
- Bring down another 0, making it 60.

14. **Divide Again**:
- 7 goes into 60 eight times (since \( 7 \times 8 = 56 \)).
- Write down 8 in the decimal part.

15. **Subtract Again**:
- Subtract 56 from 60, which gives us a remainder of 4.
- Write this as \( 60 - 56 = 4 \).

16. **Bring Down Another Zero**:
- Bring down another 0, making it 40.

17. **Divide Again**:
- 7 goes into 40 five times (since \( 7 \times 5 = 35 \)).
- Write down 5 in the decimal part.

18. **Subtract Again**:
- Subtract 35 from 40, which gives us a remainder of 5.
- Write this as \( 40 - 35 = 5 \).

19. **Bring Down Another Zero**:
- Bring down another 0, making it 50.

20. **Divide Again**:
- 7 goes into 50 seven times (since \( 7 \times 7 = 49 \)).
- Write down 7 in the decimal part.

21. **Subtract Again**:
- Subtract 49 from 50, which gives us a remainder of 1.
- Write this as \( 50 - 49 = 1 \).

22. **Notice the Pattern**:
- At this point, we see that the remainder has returned to 1, which means the decimal will start repeating from here.

23. **Write the Final Answer**:
- The decimal representation of \( \frac{22}{7} \) is \( 3.142857142857... \), which can be expressed as \( 3.142857 \overline{142857} \).

### Final Answer:
Thus, \( \frac{22}{7} = 3.142857 \overline{142857} \).