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

Explanation

To express \( \frac{13}{7} \) in decimal form, we will perform long division. Here are the steps:

### Step 1: Set up the division
We need to divide 13 by 7.

### Step 2: Divide the whole number part
7 goes into 13 one time.
- \( 7 \times 1 = 7 \)
- Subtract 7 from 13:
\[ 13 - 7 = 6 \]

### Step 3: Add a decimal point
Since we have a remainder, we can add a decimal point and a zero to the dividend (making it 60).

### Step 4: Divide the decimal part
Now, we divide 60 by 7.
- 7 goes into 60 eight times.
- \( 7 \times 8 = 56 \)
- Subtract 56 from 60:
\[ 60 - 56 = 4 \]

### Step 5: Bring down another zero
Now, we have 40 (by adding a zero to the remainder).

### Step 6: Continue dividing
7 goes into 40 five times.
- \( 7 \times 5 = 35 \)
- Subtract 35 from 40:
\[ 40 - 35 = 5 \]

### Step 7: Bring down another zero
Now, we have 50.

### Step 8: Divide again
7 goes into 50 seven times.
- \( 7 \times 7 = 49 \)
- Subtract 49 from 50:
\[ 50 - 49 = 1 \]

### Step 9: Bring down another zero
Now, we have 10.

### Step 10: Divide again
7 goes into 10 one time.
- \( 7 \times 1 = 7 \)
- Subtract 7 from 10:
\[ 10 - 7 = 3 \]

### Step 11: Bring down another zero
Now, we have 30.

### Step 12: Divide again
7 goes into 30 four times.
- \( 7 \times 4 = 28 \)
- Subtract 28 from 30:
\[ 30 - 28 = 2 \]

### Step 13: Bring down another zero
Now, we have 20.

### Step 14: Divide again
7 goes into 20 two times.
- \( 7 \times 2 = 14 \)
- Subtract 14 from 20:
\[ 20 - 14 = 6 \]

### Step 15: Notice the pattern
At this point, we notice that we are back to the remainder of 6, which we had after the first division. This means the decimal will start repeating.

### Final Result
Thus, we can express \( \frac{13}{7} \) in decimal form as:
\[ 1.857142857142\ldots \]
We can denote the repeating part as:
\[ 1.857142 \overline{857142} \]

### Summary
The decimal form of \( \frac{13}{7} \) is \( 1.857142 \) with \( 857142 \) repeating.

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