Express `(13)/(7)` in the decimal form.

Explanation

To express \( \frac{13}{7} \) in decimal form, we will perform long division. Here’s a step-by-step solution:

### Step 1: Set up the division
We want to divide 13 by 7. We can write this as \( 13 \div 7 \).

### Step 2: Perform the division
1. **First Division**:
- 7 goes into 13 one time (1).
- Multiply: \( 1 \times 7 = 7 \).
- Subtract: \( 13 - 7 = 6 \).

2. **Bring down a zero**:
- Since we have a remainder, we can bring down a zero to make it 60.

3. **Second Division**:
- 7 goes into 60 eight times (8).
- Multiply: \( 8 \times 7 = 56 \).
- Subtract: \( 60 - 56 = 4 \).

4. **Bring down another zero**:
- Bring down another zero to make it 40.

5. **Third Division**:
- 7 goes into 40 five times (5).
- Multiply: \( 5 \times 7 = 35 \).
- Subtract: \( 40 - 35 = 5 \).

6. **Bring down another zero**:
- Bring down another zero to make it 50.

7. **Fourth Division**:
- 7 goes into 50 seven times (7).
- Multiply: \( 7 \times 7 = 49 \).
- Subtract: \( 50 - 49 = 1 \).

8. **Bring down another zero**:
- Bring down another zero to make it 10.

9. **Fifth Division**:
- 7 goes into 10 one time (1).
- Multiply: \( 1 \times 7 = 7 \).
- Subtract: \( 10 - 7 = 3 \).

10. **Bring down another zero**:
- Bring down another zero to make it 30.

11. **Sixth Division**:
- 7 goes into 30 four times (4).
- Multiply: \( 4 \times 7 = 28 \).
- Subtract: \( 30 - 28 = 2 \).

12. **Bring down another zero**:
- Bring down another zero to make it 20.

13. **Seventh Division**:
- 7 goes into 20 two times (2).
- Multiply: \( 2 \times 7 = 14 \).
- Subtract: \( 20 - 14 = 6 \).

14. **Repeat**:
- We notice that we are back to a remainder of 6, which we had earlier. This indicates that the decimal will start repeating.

### Step 3: Write the result
From our divisions, we have:
- The whole number part is 1.
- The decimal part is \( 0.857142857142... \), which repeats.

Thus, we can express \( \frac{13}{7} \) in decimal form as:
\[ 1.857142857142... \]
Or using the bar notation for repeating decimals:
\[ 1.857142\overline{857142} \]

### Final Answer:
\[ \frac{13}{7} = 1.857142\overline{857142} \]

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