641097 ÷ 11 
Let's see how many times 11 fits into 641097.

Going ahead to step 1:
11 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 11

Moving on to step 2:
When dividing 64 by 11, we get 5 with a remainder of 9.
The number 5 becomes the next digit in our result. 
Result so far: 5.0
Subtract 55 from 64 to get 9.
Bring next digit (1) of the dividend behind the 9 and repeat the process: 91 / 11

On to step 3:
When dividing 91 by 11, we get 8 with a remainder of 3.
Write down 8 as next digit of the result. 
Result so far: 58.0
If we take 88 away from 91, we end up with 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 11

Let's proceed to step 4:
11 can be fit into 30 2 times, resulting in a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 582.0
If we take 22 away from 30, we end up with 8.
Include the next digit (9) from the dividend after 8, then repeat: 89 / 11

Moving on to step 5:
The number 11 fits into 89 8 times, leaving a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 5828.0
Subtract 88 from 89 to get 1.
Include the next digit (7) from the dividend after 1, then repeat: 17 / 11

Going ahead to step 6:
If we divide 17 by 11, we get 1 and a remainder of 6.
The next digit of our result is 1. 
Result so far: 58281.0
Subtracting 11 from 17 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 7:
60 divided by 11 is 5 with a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 58281.5
If we subtract 55 from 60, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 8:
When dividing 50 by 11, we get 4 with a remainder of 6.
Record the quotient 4 as the next digit in the result. 
Result so far: 58281.54
Subtract 44 from 50 to get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Let's proceed to step 9:
When dividing 60 by 11, we get 5 with a remainder of 5.
The next digit of our result is 5. 
Result so far: 58281.545
Subtracting 55 from 60 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 10:
50 divided by 11 is 4 with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 58281.5454
Deduct 44 from 50 and we're left with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

On to step 11:
If we divide 60 by 11, we get 5 and a remainder of 5.
Record the quotient 5 as the next digit in the result. 
Result so far: 58281.54545
Subtracting 55 from 60 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 12:
50 divided by 11 is 4 with a remainder of 6.
The number 4 becomes the next digit in our result. 
Result so far: 58281.545454
Subtracting 44 from 50 leaves us with 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 13:
When dividing 60 by 11, we get 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 58281.5454545
Deduct 55 from 60 and we're left with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 14:
11 goes into 50 4 times with a remainder of 6.
Write down 4 as next digit of the result. 
Result so far: 58281.54545454
If we subtract 44 from 50, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

In conclusion, the division gives 58281.54545454 with a balance of 6e-09.