We look at the division of 109638 by 51 
We want to divide 109638 by 51.

Advancing to step 1:
1 divided by 51 is 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 51

Step 2:
10 divided by 51 is 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 51

On to step 3:
51 goes into 109 2 times with a remainder of 7.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 102 from 109 leaves us with 7.
Grab the next digit (6) from the dividend, add it to 7, then carry on: 76 / 51

Let's proceed to step 4:
When dividing 76 by 51, we get 1 with a remainder of 25.
Write down 1 as next digit of the result. 
Result so far: 21.0
Deduct 51 from 76 and we're left with 25.
Fetch the next digit (3) from the dividend, attach it to 25 and continue: 253 / 51

Let's proceed to step 5:
The number 51 fits into 253 4 times, leaving a remainder of 49.
The next digit of our result is 4. 
Result so far: 214.0
Deduct 204 from 253 and we're left with 49.
Append the next digit (8) from the dividend to 49 and continue with: 498 / 51

Moving on to step 6:
If we divide 498 by 51, we get 9 and a remainder of 39.
The next digit of our result is 9. 
Result so far: 2149.0
Subtracting 459 from 498 leaves us with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

Going ahead to step 7:
390 divided by 51 is 7 with a remainder of 33.
Record the quotient 7 as the next digit in the result. 
Result so far: 2149.7
The remainder is 33 after subtracting 357 from 390.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 8:
51 can be fit into 330 6 times, resulting in a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 2149.76
If we take 306 away from 330, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 9:
51 can be fit into 240 4 times, resulting in a remainder of 36.
Record the quotient 4 as the next digit in the result. 
Result so far: 2149.764
The remainder is 36 after subtracting 204 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

On to step 10:
51 goes into 360 7 times with a remainder of 3.
Write down 7 as next digit of the result. 
Result so far: 2149.7647
Deduct 357 from 360 and we're left with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Moving on to step 11:
51 goes into 30 0 times with a remainder of 30.
The next digit of our result is 0. 
Result so far: 2149.7647
Subtracting 0 from 30 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Moving on to step 12:
If we divide 300 by 51, we get 5 and a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 2149.764705
If we take 255 away from 300, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 13:
The number 51 fits into 450 8 times, leaving a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 2149.7647058
Subtracting 408 from 450 leaves us with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Going ahead to step 14:
420 divided by 51 is 8 with a remainder of 12.
Use 8 as the next digit of our solution. 
Result so far: 2149.76470588
Deduct 408 from 420 and we're left with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 2149.76470588 with a balance of 1.2e-08.