Represent the following as decimal numbers :
`(12)/(7)`

Answer

To represent \( \frac{12}{7} \) as a decimal number, we will perform the division of 12 by 7 step by step.

### Step 1: Set up the division
We start by dividing 12 by 7. Here, 12 is the dividend and 7 is the divisor.

### Step 2: Perform the division
1. **How many times does 7 go into 12?**
- 7 goes into 12 one time (1).
- \( 7 \times 1 = 7 \)
- Subtract 7 from 12:
\[ 12 - 7 = 5 \]

### Step 3: Add a decimal point
Since we have a remainder, we will add a decimal point to the quotient and a zero to the remainder to continue the division.
- The quotient so far is 1. Now we bring down a 0 making it 50.

### Step 4: Continue the division
2. **How many times does 7 go into 50?**
- 7 goes into 50 seven times (7).
- \( 7 \times 7 = 49 \)
- Subtract 49 from 50:
\[ 50 - 49 = 1 \]

### Step 5: Bring down another zero
Now, we bring down another 0 making it 10.

### Step 6: Continue the division
3. **How many times does 7 go into 10?**
- 7 goes into 10 one time (1).
- \( 7 \times 1 = 7 \)
- Subtract 7 from 10:
\[ 10 - 7 = 3 \]

### Step 7: Bring down another zero
Now, we bring down another 0 making it 30.

### Step 8: Continue the division
4. **How many times does 7 go into 30?**
- 7 goes into 30 four times (4).
- \( 7 \times 4 = 28 \)
- Subtract 28 from 30:
\[ 30 - 28 = 2 \]

### Step 9: Bring down another zero
Now, we bring down another 0 making it 20.

### Step 10: Continue the division
5. **How many times does 7 go into 20?**
- 7 goes into 20 two times (2).
- \( 7 \times 2 = 14 \)
- Subtract 14 from 20:
\[ 20 - 14 = 6 \]

### Step 11: Bring down another zero
Now, we bring down another 0 making it 60.

### Step 12: Continue the division
6. **How many times does 7 go into 60?**
- 7 goes into 60 eight times (8).
- \( 7 \times 8 = 56 \)
- Subtract 56 from 60:
\[ 60 - 56 = 4 \]

### Step 13: Bring down another zero
Now, we bring down another 0 making it 40.

### Step 14: Continue the division
7. **How many times does 7 go into 40?**
- 7 goes into 40 five times (5).
- \( 7 \times 5 = 35 \)
- Subtract 35 from 40:
\[ 40 - 35 = 5 \]

### Step 15: Repeat the process
At this point, we notice that we are back to a remainder of 5, which we have seen before. This indicates that the decimal will start repeating.

### Final Result
Putting it all together, we have:
\[ \frac{12}{7} = 1.714285714285... \]
This can be expressed as:
\[ 1.\overline{714285} \]