Let's divide 81908569 by 678
Our goal is to divide 81908569 by 678.

On to step 1:
When dividing 8 by 678, we get 0 with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Grab the next digit (1) from the dividend, add it to 8, then carry on: 81 / 678

Going ahead to step 2:
When dividing 81 by 678, we get 0 with a remainder of 81.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 81 to get 81.
Include the next digit (9) from the dividend after 81, then repeat: 819 / 678

Advancing to step 3:
678 can be fit into 819 1 times, resulting in a remainder of 141.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 678 from 819, we get 141.
Fetch the next digit (0) from the dividend, attach it to 141 and continue: 1410 / 678

On to step 4:
678 goes into 1410 2 times with a remainder of 54.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we take 1356 away from 1410, we end up with 54.
Fetch the next digit (8) from the dividend, attach it to 54 and continue: 548 / 678

Advancing to step 5:
678 goes into 548 0 times with a remainder of 548.
The number 0 becomes the next digit in our result. 
Result so far: 120.0
The remainder is 548 after subtracting 0 from 548.
Bring next digit (5) of the dividend behind the 548 and repeat the process: 5485 / 678

Advancing to step 6:
If we divide 5485 by 678, we get 8 and a remainder of 61.
The next digit of our result is 8. 
Result so far: 1208.0
Deduct 5424 from 5485 and we're left with 61.
Append the next digit (6) from the dividend to 61 and continue with: 616 / 678

On to step 7:
If we divide 616 by 678, we get 0 and a remainder of 616.
Put 0 as the next digit of the answer. 
Result so far: 12080.0
Deduct 0 from 616 and we're left with 616.
Include the next digit (9) from the dividend after 616, then repeat: 6169 / 678

Let's proceed to step 8:
The number 678 fits into 6169 9 times, leaving a remainder of 67.
The next digit of our result is 9. 
Result so far: 120809.0
The remainder is 67 after subtracting 6102 from 6169.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 9:
If we divide 670 by 678, we get 0 and a remainder of 670.
Record the quotient 0 as the next digit in the result. 
Result so far: 120809.0
The remainder is 670 after subtracting 0 from 670.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6700, and continue the process.

Moving on to step 10:
If we divide 6700 by 678, we get 9 and a remainder of 598.
Use 9 as the next digit of our solution. 
Result so far: 120809.09
If we take 6102 away from 6700, we end up with 598.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5980, and continue the process.

Let's proceed to step 11:
When dividing 5980 by 678, we get 8 with a remainder of 556.
Use 8 as the next digit of our solution. 
Result so far: 120809.098
Deduct 5424 from 5980 and we're left with 556.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5560, and continue the process.

Moving on to step 12:
5560 divided by 678 is 8 with a remainder of 136.
The number 8 becomes the next digit in our result. 
Result so far: 120809.0988
If we subtract 5424 from 5560, we get 136.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1360, and continue the process.

After the division, we end up with 120809.0988 and a remainder of 0.00136.