Find the decimal representation of `(22)/7`

Explanation

To find the decimal representation of \( \frac{22}{7} \), we will perform long division.

### Step 1: Set up the long division
We need to divide 22 by 7. Write 22 as 22.000000 (adding decimal places for better accuracy).

### Step 2: Divide 22 by 7
- 7 goes into 22 three times (since \( 7 \times 3 = 21 \)).
- Write 3 above the division line.

### Step 3: Subtract
- Subtract \( 21 \) from \( 22 \), which gives us \( 1 \).
- Bring down the next 0 (making it 10).

### Step 4: Divide 10 by 7
- 7 goes into 10 once (since \( 7 \times 1 = 7 \)).
- Write 1 next to 3 above the division line.

### Step 5: Subtract again
- Subtract \( 7 \) from \( 10 \), which gives us \( 3 \).
- Bring down the next 0 (making it 30).

### Step 6: Divide 30 by 7
- 7 goes into 30 four times (since \( 7 \times 4 = 28 \)).
- Write 4 next to 31 above the division line.

### Step 7: Subtract again
- Subtract \( 28 \) from \( 30 \), which gives us \( 2 \).
- Bring down the next 0 (making it 20).

### Step 8: Divide 20 by 7
- 7 goes into 20 two times (since \( 7 \times 2 = 14 \)).
- Write 2 next to 314 above the division line.

### Step 9: Subtract again
- Subtract \( 14 \) from \( 20 \), which gives us \( 6 \).
- Bring down the next 0 (making it 60).

### Step 10: Divide 60 by 7
- 7 goes into 60 eight times (since \( 7 \times 8 = 56 \)).
- Write 8 next to 3142 above the division line.

### Step 11: Subtract again
- Subtract \( 56 \) from \( 60 \), which gives us \( 4 \).
- Bring down the next 0 (making it 40).

### Step 12: Divide 40 by 7
- 7 goes into 40 five times (since \( 7 \times 5 = 35 \)).
- Write 5 next to 31428 above the division line.

### Step 13: Subtract again
- Subtract \( 35 \) from \( 40 \), which gives us \( 5 \).
- Bring down the next 0 (making it 50).

### Step 14: Divide 50 by 7
- 7 goes into 50 seven times (since \( 7 \times 7 = 49 \)).
- Write 7 next to 314285 above the division line.

### Step 15: Subtract again
- Subtract \( 49 \) from \( 50 \), which gives us \( 1 \).
- Bring down the next 0 (making it 10).

### Step 16: Repeat the process
Notice that we are back to dividing 10 by 7, which will repeat the cycle.

### Final Result
The decimal representation of \( \frac{22}{7} \) is \( 3.142857142857... \), which is a repeating decimal.

### Summary
Thus, \( \frac{22}{7} \) in decimal form is approximately \( 3.142857 \) (with 142857 repeating).

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