We're dividing 642974 by 51 
We want to divide 642974 by 51.

On to step 1:
51 can be fit into 6 0 times, resulting in a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 51

On to step 2:
64 divided by 51 is 1 with a remainder of 13.
Use 1 as the next digit of our solution. 
Result so far: 1.0
The remainder is 13 after subtracting 51 from 64.
Include the next digit (2) from the dividend after 13, then repeat: 132 / 51

On to step 3:
If we divide 132 by 51, we get 2 and a remainder of 30.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
If we take 102 away from 132, we end up with 30.
Append the next digit (9) from the dividend to 30 and continue with: 309 / 51

Going ahead to step 4:
309 divided by 51 is 6 with a remainder of 3.
The next digit of our result is 6. 
Result so far: 126.0
Subtract 306 from 309 to get 3.
Take the next digit (7) from the dividend and append it to 3, then repeat: 37 / 51

Let's proceed to step 5:
If we divide 37 by 51, we get 0 and a remainder of 37.
The next digit of our result is 0. 
Result so far: 1260.0
The remainder is 37 after subtracting 0 from 37.
Include the next digit (4) from the dividend after 37, then repeat: 374 / 51

Moving on to step 6:
The number 51 fits into 374 7 times, leaving a remainder of 17.
Use 7 as the next digit of our solution. 
Result so far: 12607.0
If we subtract 357 from 374, we get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 7:
The number 51 fits into 170 3 times, leaving a remainder of 17.
Write down 3 as next digit of the result. 
Result so far: 12607.3
Subtract 153 from 170 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

On to step 8:
51 can be fit into 170 3 times, resulting in a remainder of 17.
Record the quotient 3 as the next digit in the result. 
Result so far: 12607.33
The remainder is 17 after subtracting 153 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

In conclusion, the division gives 12607.33 with a balance of 0.017.