Let's divide 100111 by 90
We're looking to find how many times 90 goes into 100111.

Let's proceed to step 1:
The number 90 fits into 1 0 times, leaving a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 90

Step 2:
If we divide 10 by 90, we get 0 and 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.
Append the next digit (0) from the dividend to 10 and continue with: 100 / 90

Going ahead to step 3:
90 goes into 100 1 times with a remainder of 10.
Write down 1 as next digit of the result. 
Result so far: 1.0
Deduct 90 from 100 and we're left with 10.
Take the next digit (1) from the dividend and append it to 10, then repeat: 101 / 90

Moving on to step 4:
If we divide 101 by 90, we get 1 and a remainder of 11.
The next digit of our result is 1. 
Result so far: 11.0
If we take 90 away from 101, we end up with 11.
Take the next digit (1) from the dividend and append it to 11, then repeat: 111 / 90

Moving on to step 5:
The number 90 fits into 111 1 times, leaving a remainder of 21.
Use 1 as the next digit of our solution. 
Result so far: 111.0
The remainder is 21 after subtracting 90 from 111.
Take the next digit (1) from the dividend and append it to 21, then repeat: 211 / 90

Moving on to step 6:
When dividing 211 by 90, we get 2 with a remainder of 31.
Record the quotient 2 as the next digit in the result. 
Result so far: 1112.0
Subtracting 180 from 211 leaves us 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.

Moving on to step 7:
90 goes into 310 3 times with a remainder of 40.
The next digit of our result is 3. 
Result so far: 1112.3
The remainder is 40 after subtracting 270 from 310.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 8:
400 divided by 90 is 4 with a remainder of 40.
Record the quotient 4 as the next digit in the result. 
Result so far: 1112.34
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.

Advancing to step 9:
The number 90 fits into 400 4 times, leaving a remainder of 40.
Record the quotient 4 as the next digit in the result. 
Result so far: 1112.344
If we subtract 360 from 400, we 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.

The quotient of the division is 1112.344, and the remainder is 0.004.