We're dividing 677984 by 11 
We want to figure out the number of times 677984 can be divided by 11.

Advancing to step 1:
11 goes into 6 0 times with a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 11

Step 2:
When dividing 67 by 11, we get 6 with a remainder of 1.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 66 from 67 to get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 11

On to step 3:
When dividing 17 by 11, we get 1 with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 61.0
Subtract 11 from 17 to get 6.
Append the next digit (9) from the dividend to 6 and continue with: 69 / 11

Moving on to step 4:
11 can be fit into 69 6 times, resulting in a remainder of 3.
Use 6 as the next digit of our solution. 
Result so far: 616.0
Deduct 66 from 69 and we're left with 3.
Bring next digit (8) of the dividend behind the 3 and repeat the process: 38 / 11

Moving on to step 5:
If we divide 38 by 11, we get 3 and a remainder of 5.
Write down 3 as next digit of the result. 
Result so far: 6163.0
Subtracting 33 from 38 leaves us with 5.
Append the next digit (4) from the dividend to 5 and continue with: 54 / 11

Moving on to step 6:
11 can be fit into 54 4 times, resulting in a remainder of 10.
Put 4 as the next digit of the answer. 
Result so far: 61634.0
The remainder is 10 after subtracting 44 from 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 7:
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: 61634.9
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.

On to step 8:
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: 61634.9
If we subtract 0 from 10, we 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.

Moving on to step 9:
When dividing 100 by 11, we get 9 with a remainder of 1.
The next digit of our result is 9. 
Result so far: 61634.909
The remainder is 1 after subtracting 99 from 100.
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 10:
11 can be fit into 10 0 times, resulting in a remainder of 10.
The next digit of our result is 0. 
Result so far: 61634.909
Subtracting 0 from 10 leaves us 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.

Advancing to step 11:
The number 11 fits into 100 9 times, leaving a remainder of 1.
Use 9 as the next digit of our solution. 
Result so far: 61634.90909
The remainder is 1 after subtracting 99 from 100.
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 12:
When dividing 10 by 11, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 61634.90909
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.

Let's proceed to step 13:
11 goes into 100 9 times with a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 61634.9090909
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.

Let's proceed to step 14:
When dividing 10 by 11, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 61634.9090909
If we subtract 0 from 10, we 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.

In conclusion, the division gives 61634.9090909 with a balance of 1e-08.