Let's divide 126100 by 9
We're looking to find how many times 9 goes into 126100.

Advancing to step 1:
9 goes into 1 0 times with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 9

Advancing to step 2:
When dividing 12 by 9, we get 1 with a remainder of 3.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 9 from 12, we get 3.
Include the next digit (6) from the dividend after 3, then repeat: 36 / 9

On to step 3:
If we divide 36 by 9, we get 4 and a remainder of 0.
Record the quotient 4 as the next digit in the result. 
Result so far: 14.0
If we take 36 away from 36, we end up with 0.
Include the next digit (1) from the dividend after 0, then repeat: 1 / 9

On to step 4:
If we divide 1 by 9, we get 0 and a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 140.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 9

Moving on to step 5:
When dividing 10 by 9, we get 1 with a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 1401.0
If we take 9 away from 10, we end up with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 9

Step 6:
9 can be fit into 10 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 14011.0
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Going ahead to step 7:
If we divide 10 by 9, we get 1 and a remainder of 1.
The number 1 becomes the next digit in our result. 
Result so far: 14011.1
Subtract 9 from 10 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 8:
If we divide 10 by 9, we get 1 and a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 14011.11
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 14011.11, and the remainder is 0.001.