We look at the division of 100681 by 511 
We want to divide 100681 by 511.

Moving on to step 1:
1 divided by 511 is 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 511

Going ahead to step 2:
The number 511 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Take the next digit (0) from the dividend and append it to 10, then repeat: 100 / 511

On to step 3:
100 divided by 511 is 0 with a remainder of 100.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 100 and we're left with 100.
Append the next digit (6) from the dividend to 100 and continue with: 1006 / 511

Advancing to step 4:
The number 511 fits into 1006 1 times, leaving a remainder of 495.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we take 511 away from 1006, we end up with 495.
Include the next digit (8) from the dividend after 495, then repeat: 4958 / 511

Let's proceed to step 5:
511 can be fit into 4958 9 times, resulting in a remainder of 359.
Write down 9 as next digit of the result. 
Result so far: 19.0
If we take 4599 away from 4958, we end up with 359.
Include the next digit (1) from the dividend after 359, then repeat: 3591 / 511

Let's proceed to step 6:
3591 divided by 511 is 7 with a remainder of 14.
Put 7 as the next digit of the answer. 
Result so far: 197.0
Subtracting 3577 from 3591 leaves us with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 7:
140 divided by 511 is 0 with a remainder of 140.
Write down 0 as next digit of the result. 
Result so far: 197.0
If we subtract 0 from 140, we get 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1400, and continue the process.

Step 8:
When dividing 1400 by 511, we get 2 with a remainder of 378.
The next digit of our result is 2. 
Result so far: 197.02
If we subtract 1022 from 1400, we get 378.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3780, and continue the process.

On to step 9:
3780 divided by 511 is 7 with a remainder of 203.
Put 7 as the next digit of the answer. 
Result so far: 197.027
If we subtract 3577 from 3780, we get 203.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2030, and continue the process.

Moving on to step 10:
511 can be fit into 2030 3 times, resulting in a remainder of 497.
The number 3 becomes the next digit in our result. 
Result so far: 197.0273
If we take 1533 away from 2030, we end up with 497.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4970, and continue the process.

Let's proceed to step 11:
When dividing 4970 by 511, we get 9 with a remainder of 371.
Write down 9 as next digit of the result. 
Result so far: 197.02739
Subtracting 4599 from 4970 leaves us with 371.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3710, and continue the process.

Let's proceed to step 12:
If we divide 3710 by 511, we get 7 and a remainder of 133.
Record the quotient 7 as the next digit in the result. 
Result so far: 197.027397
Subtract 3577 from 3710 to get 133.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1330, and continue the process.

Moving on to step 13:
If we divide 1330 by 511, we get 2 and a remainder of 308.
The next digit of our result is 2. 
Result so far: 197.0273972
The remainder is 308 after subtracting 1022 from 1330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3080, and continue the process.

On to step 14:
When dividing 3080 by 511, we get 6 with a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 197.02739726
If we take 3066 away from 3080, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

After the division, we end up with 197.02739726 and a remainder of 1.4e-08.