We're dividing 681108 by 89 
We're looking to find how many times 89 goes into 681108.

Advancing to step 1:
The number 89 fits into 6 0 times, leaving a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Bring next digit (8) of the dividend behind the 6 and repeat the process: 68 / 89

Moving on to step 2:
89 can be fit into 68 0 times, resulting in a remainder of 68.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 68 to get 68.
Bring next digit (1) of the dividend behind the 68 and repeat the process: 681 / 89

Let's proceed to step 3:
The number 89 fits into 681 7 times, leaving a remainder of 58.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
The remainder is 58 after subtracting 623 from 681.
Take the next digit (1) from the dividend and append it to 58, then repeat: 581 / 89

Moving on to step 4:
If we divide 581 by 89, we get 6 and a remainder of 47.
Put 6 as the next digit of the answer. 
Result so far: 76.0
Subtract 534 from 581 to get 47.
Grab the next digit (0) from the dividend, add it to 47, then carry on: 470 / 89

Step 5:
89 can be fit into 470 5 times, resulting in a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 765.0
Subtract 445 from 470 to get 25.
Grab the next digit (8) from the dividend, add it to 25, then carry on: 258 / 89

Step 6:
89 goes into 258 2 times with a remainder of 80.
Use 2 as the next digit of our solution. 
Result so far: 7652.0
Deduct 178 from 258 and we're left with 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Advancing to step 7:
800 divided by 89 is 8 with a remainder of 88.
Write down 8 as next digit of the result. 
Result so far: 7652.8
If we subtract 712 from 800, we get 88.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Moving on to step 8:
89 goes into 880 9 times with a remainder of 79.
The next digit of our result is 9. 
Result so far: 7652.89
If we take 801 away from 880, we end up with 79.
Since there are no more digits in the dividend, we add a zero to the remainder making it 790, and continue the process.

On to step 9:
The number 89 fits into 790 8 times, leaving a remainder of 78.
Put 8 as the next digit of the answer. 
Result so far: 7652.898
Subtracting 712 from 790 leaves us with 78.
Since there are no more digits in the dividend, we add a zero to the remainder making it 780, and continue the process.

Moving on to step 10:
780 divided by 89 is 8 with a remainder of 68.
The next digit of our result is 8. 
Result so far: 7652.8988
If we subtract 712 from 780, we get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

The final outcome is 7652.8988, with a leftover of 0.00068.