We look at the division of 199634 by 45 
We want to divide 199634 by 45.

Step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Bring next digit (9) of the dividend behind the 1 and repeat the process: 19 / 45

Moving on to step 2:
19 divided by 45 is 0 with a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 19, we get 19.
Bring next digit (9) of the dividend behind the 19 and repeat the process: 199 / 45

Going ahead to step 3:
If we divide 199 by 45, we get 4 and a remainder of 19.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Subtracting 180 from 199 leaves us with 19.
Append the next digit (6) from the dividend to 19 and continue with: 196 / 45

Advancing to step 4:
196 divided by 45 is 4 with a remainder of 16.
Write down 4 as next digit of the result. 
Result so far: 44.0
Subtract 180 from 196 to get 16.
Take the next digit (3) from the dividend and append it to 16, then repeat: 163 / 45

Advancing to step 5:
45 goes into 163 3 times with a remainder of 28.
The number 3 becomes the next digit in our result. 
Result so far: 443.0
Subtract 135 from 163 to get 28.
Take the next digit (4) from the dividend and append it to 28, then repeat: 284 / 45

On to step 6:
The number 45 fits into 284 6 times, leaving a remainder of 14.
The next digit of our result is 6. 
Result so far: 4436.0
If we take 270 away from 284, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Let's proceed to step 7:
45 goes into 140 3 times with a remainder of 5.
The next digit of our result is 3. 
Result so far: 4436.3
The remainder is 5 after subtracting 135 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 8:
50 divided by 45 is 1 with a remainder of 5.
The next digit of our result is 1. 
Result so far: 4436.31
If we subtract 45 from 50, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Let's proceed to step 9:
If we divide 50 by 45, we get 1 and a remainder of 5.
Put 1 as the next digit of the answer. 
Result so far: 4436.311
If we take 45 away from 50, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The quotient of the division is 4436.311, and the remainder is 0.0005.