We're dividing 814205 by 45 
We want to figure out the number of times 814205 can be divided by 45.

Advancing to step 1:
If we divide 8 by 45, we get 0 and a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Grab the next digit (1) from the dividend, add it to 8, then carry on: 81 / 45

Going ahead to step 2:
45 can be fit into 81 1 times, resulting in a remainder of 36.
Use 1 as the next digit of our solution. 
Result so far: 1.0
If we subtract 45 from 81, we get 36.
Include the next digit (4) from the dividend after 36, then repeat: 364 / 45

Moving on to step 3:
The number 45 fits into 364 8 times, leaving a remainder of 4.
Write down 8 as next digit of the result. 
Result so far: 18.0
If we subtract 360 from 364, we get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 45

Going ahead to step 4:
When dividing 42 by 45, we get 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 180.0
The remainder is 42 after subtracting 0 from 42.
Fetch the next digit (0) from the dividend, attach it to 42 and continue: 420 / 45

Moving on to step 5:
45 can be fit into 420 9 times, resulting in a remainder of 15.
The number 9 becomes the next digit in our result. 
Result so far: 1809.0
Deduct 405 from 420 and we're left with 15.
Fetch the next digit (5) from the dividend, attach it to 15 and continue: 155 / 45

Step 6:
The number 45 fits into 155 3 times, leaving a remainder of 20.
The number 3 becomes the next digit in our result. 
Result so far: 18093.0
Subtracting 135 from 155 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 7:
200 divided by 45 is 4 with a remainder of 20.
Record the quotient 4 as the next digit in the result. 
Result so far: 18093.4
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Step 8:
200 divided by 45 is 4 with a remainder of 20.
Put 4 as the next digit of the answer. 
Result so far: 18093.44
If we subtract 180 from 200, we get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

The final result is 18093.44 with a remainder of 0.02.