We're dividing 99634 by 51 
Our goal is to divide 99634 by 51.

On to step 1:
When dividing 9 by 51, we get 0 with a remainder of 9.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Take the next digit (9) from the dividend and append it to 9, then repeat: 99 / 51

Let's proceed to step 2:
If we divide 99 by 51, we get 1 and a remainder of 48.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtract 51 from 99 to get 48.
Take the next digit (6) from the dividend and append it to 48, then repeat: 486 / 51

On to step 3:
51 goes into 486 9 times with a remainder of 27.
Use 9 as the next digit of our solution. 
Result so far: 19.0
If we take 459 away from 486, we end up with 27.
Take the next digit (3) from the dividend and append it to 27, then repeat: 273 / 51

Going ahead to step 4:
51 can be fit into 273 5 times, resulting in a remainder of 18.
Put 5 as the next digit of the answer. 
Result so far: 195.0
If we subtract 255 from 273, we get 18.
Include the next digit (4) from the dividend after 18, then repeat: 184 / 51

Step 5:
When dividing 184 by 51, we get 3 with a remainder of 31.
The number 3 becomes the next digit in our result. 
Result so far: 1953.0
Subtracting 153 from 184 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 6:
51 goes into 310 6 times with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 1953.6
Subtract 306 from 310 to get 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Let's proceed to step 7:
51 can be fit into 40 0 times, resulting in a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 1953.6
Deduct 0 from 40 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 8:
51 goes into 400 7 times with a remainder of 43.
The number 7 becomes the next digit in our result. 
Result so far: 1953.607
Subtracting 357 from 400 leaves us with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 9:
51 can be fit into 430 8 times, resulting in a remainder of 22.
The number 8 becomes the next digit in our result. 
Result so far: 1953.6078
The remainder is 22 after subtracting 408 from 430.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Step 10:
51 goes into 220 4 times with a remainder of 16.
The number 4 becomes the next digit in our result. 
Result so far: 1953.60784
The remainder is 16 after subtracting 204 from 220.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Step 11:
160 divided by 51 is 3 with a remainder of 7.
Write down 3 as next digit of the result. 
Result so far: 1953.607843
If we subtract 153 from 160, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 12:
70 divided by 51 is 1 with a remainder of 19.
The next digit of our result is 1. 
Result so far: 1953.6078431
If we take 51 away from 70, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Moving on to step 13:
190 divided by 51 is 3 with a remainder of 37.
The next digit of our result is 3. 
Result so far: 1953.60784313
If we subtract 153 from 190, we get 37.
Since there are no more digits in the dividend, we add a zero to the remainder making it 370, and continue the process.

In conclusion, the division gives 1953.60784313 with a balance of 3.7e-08.