10121 ÷ 99 
Our goal is to divide 10121 by 99.

Advancing to step 1:
When dividing 1 by 99, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 99

On to step 2:
If we divide 10 by 99, we get 0 and a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Grab the next digit (1) from the dividend, add it to 10, then carry on: 101 / 99

Let's proceed to step 3:
101 divided by 99 is 1 with a remainder of 2.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Deduct 99 from 101 and we're left with 2.
Include the next digit (2) from the dividend after 2, then repeat: 22 / 99

Let's proceed to step 4:
22 divided by 99 is 0 with a remainder of 22.
The next digit of our result is 0. 
Result so far: 10.0
Subtract 0 from 22 to get 22.
Grab the next digit (1) from the dividend, add it to 22, then carry on: 221 / 99

Let's proceed to step 5:
99 goes into 221 2 times with a remainder of 23.
The next digit of our result is 2. 
Result so far: 102.0
If we subtract 198 from 221, we get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Step 6:
230 divided by 99 is 2 with a remainder of 32.
Put 2 as the next digit of the answer. 
Result so far: 102.2
Subtract 198 from 230 to get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 7:
When dividing 320 by 99, we get 3 with a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 102.23
Subtract 297 from 320 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 8:
230 divided by 99 is 2 with a remainder of 32.
The next digit of our result is 2. 
Result so far: 102.232
Deduct 198 from 230 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

On to step 9:
320 divided by 99 is 3 with a remainder of 23.
Write down 3 as next digit of the result. 
Result so far: 102.2323
Subtract 297 from 320 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 10:
The number 99 fits into 230 2 times, leaving a remainder of 32.
The next digit of our result is 2. 
Result so far: 102.23232
Deduct 198 from 230 and we're left with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Going ahead to step 11:
320 divided by 99 is 3 with a remainder of 23.
Use 3 as the next digit of our solution. 
Result so far: 102.232323
If we take 297 away from 320, we end up with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 12:
230 divided by 99 is 2 with a remainder of 32.
The next digit of our result is 2. 
Result so far: 102.2323232
If we take 198 away from 230, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 13:
If we divide 320 by 99, we get 3 and a remainder of 23.
The next digit of our result is 3. 
Result so far: 102.23232323
Subtract 297 from 320 to get 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Our division results in 102.23232323 with a remaining 2.3e-08.