We're dividing 976581 by 11 
We want to divide 976581 by 11.

Moving on to step 1:
11 can be fit into 9 0 times, resulting in a remainder of 9.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Fetch the next digit (7) from the dividend, attach it to 9 and continue: 97 / 11

Advancing to step 2:
11 goes into 97 8 times with a remainder of 9.
Record the quotient 8 as the next digit in the result. 
Result so far: 8.0
If we take 88 away from 97, we end up with 9.
Include the next digit (6) from the dividend after 9, then repeat: 96 / 11

Going ahead to step 3:
11 can be fit into 96 8 times, resulting in a remainder of 8.
Record the quotient 8 as the next digit in the result. 
Result so far: 88.0
Subtracting 88 from 96 leaves us with 8.
Fetch the next digit (5) from the dividend, attach it to 8 and continue: 85 / 11

Step 4:
11 can be fit into 85 7 times, resulting in a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 887.0
If we subtract 77 from 85, we get 8.
Take the next digit (8) from the dividend and append it to 8, then repeat: 88 / 11

Let's proceed to step 5:
When dividing 88 by 11, we get 8 with a remainder of 0.
Write down 8 as next digit of the result. 
Result so far: 8878.0
If we subtract 88 from 88, we get 0.
Bring next digit (1) of the dividend behind the 0 and repeat the process: 1 / 11

On to step 6:
1 divided by 11 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 88780.0
Subtract 0 from 1 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 7:
If we divide 10 by 11, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 88780.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 8:
If we divide 100 by 11, we get 9 and a remainder of 1.
The next digit of our result is 9. 
Result so far: 88780.09
If we take 99 away from 100, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 9:
10 divided by 11 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 88780.09
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 10:
If we divide 100 by 11, we get 9 and a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 88780.0909
If we subtract 99 from 100, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 11:
11 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 88780.0909
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

On to step 12:
If we divide 100 by 11, we get 9 and a remainder of 1.
Write down 9 as next digit of the result. 
Result so far: 88780.090909
Deduct 99 from 100 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 13:
If we divide 10 by 11, we get 0 and a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 88780.090909
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 14:
When dividing 100 by 11, we get 9 with a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 88780.09090909
Subtract 99 from 100 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 88780.09090909 with a balance of 1e-09.