Let's divide 101821 by 90
We want to figure out the number of times 101821 can be divided by 90.

Step 1:
90 can be fit into 1 0 times, resulting in a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 90

On to step 2:
90 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 10 and we're left with 10.
Fetch the next digit (1) from the dividend, attach it to 10 and continue: 101 / 90

Advancing to step 3:
101 divided by 90 is 1 with a remainder of 11.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtract 90 from 101 to get 11.
Take the next digit (8) from the dividend and append it to 11, then repeat: 118 / 90

Moving on to step 4:
The number 90 fits into 118 1 times, leaving a remainder of 28.
Use 1 as the next digit of our solution. 
Result so far: 11.0
Deduct 90 from 118 and we're left with 28.
Take the next digit (2) from the dividend and append it to 28, then repeat: 282 / 90

Going ahead to step 5:
90 can be fit into 282 3 times, resulting in a remainder of 12.
The next digit of our result is 3. 
Result so far: 113.0
Subtracting 270 from 282 leaves us with 12.
Grab the next digit (1) from the dividend, add it to 12, then carry on: 121 / 90

Going ahead to step 6:
90 goes into 121 1 times with a remainder of 31.
Use 1 as the next digit of our solution. 
Result so far: 1131.0
If we take 90 away from 121, we end up with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 7:
If we divide 310 by 90, we get 3 and a remainder of 40.
Write down 3 as next digit of the result. 
Result so far: 1131.3
Subtract 270 from 310 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 8:
If we divide 400 by 90, we get 4 and a remainder of 40.
Put 4 as the next digit of the answer. 
Result so far: 1131.34
Subtracting 360 from 400 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 9:
When dividing 400 by 90, we get 4 with a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 1131.344
Deduct 360 from 400 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

In conclusion, the division gives 1131.344 with a balance of 0.004.