We divide 108821 by 11
We're looking to find how many times 11 goes into 108821.

Advancing to step 1:
When dividing 1 by 11, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 11

Advancing to step 2:
The number 11 fits into 10 0 times, leaving a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Grab the next digit (8) from the dividend, add it to 10, then carry on: 108 / 11

Moving on to step 3:
When dividing 108 by 11, we get 9 with a remainder of 9.
Use 9 as the next digit of our solution. 
Result so far: 9.0
Subtract 99 from 108 to get 9.
Grab the next digit (8) from the dividend, add it to 9, then carry on: 98 / 11

Step 4:
11 can be fit into 98 8 times, resulting in a remainder of 10.
Use 8 as the next digit of our solution. 
Result so far: 98.0
The remainder is 10 after subtracting 88 from 98.
Grab the next digit (2) from the dividend, add it to 10, then carry on: 102 / 11

Advancing to step 5:
If we divide 102 by 11, we get 9 and a remainder of 3.
Use 9 as the next digit of our solution. 
Result so far: 989.0
If we subtract 99 from 102, we get 3.
Grab the next digit (1) from the dividend, add it to 3, then carry on: 31 / 11

Going ahead to step 6:
When dividing 31 by 11, we get 2 with a remainder of 9.
Use 2 as the next digit of our solution. 
Result so far: 9892.0
If we subtract 22 from 31, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 7:
The number 11 fits into 90 8 times, leaving a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 9892.8
Subtract 88 from 90 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
20 divided by 11 is 1 with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 9892.81
If we subtract 11 from 20, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 9:
When dividing 90 by 11, we get 8 with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 9892.818
Subtract 88 from 90 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 10:
When dividing 20 by 11, we get 1 with a remainder of 9.
The next digit of our result is 1. 
Result so far: 9892.8181
The remainder is 9 after subtracting 11 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Moving on to step 11:
90 divided by 11 is 8 with a remainder of 2.
Use 8 as the next digit of our solution. 
Result so far: 9892.81818
If we subtract 88 from 90, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Step 12:
If we divide 20 by 11, we get 1 and a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 9892.818181
If we subtract 11 from 20, we get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 13:
90 divided by 11 is 8 with a remainder of 2.
Record the quotient 8 as the next digit in the result. 
Result so far: 9892.8181818
The remainder is 2 after subtracting 88 from 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Going ahead to step 14:
When dividing 20 by 11, we get 1 with a remainder of 9.
Write down 1 as next digit of the result. 
Result so far: 9892.81818181
The remainder is 9 after subtracting 11 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Our division results in 9892.81818181 with a remaining 9e-09.