We're dividing 188219 by 45 
We want to divide 188219 by 45.

Moving on to step 1:
1 divided by 45 is 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Fetch the next digit (8) from the dividend, attach it to 1 and continue: 18 / 45

Advancing to step 2:
When dividing 18 by 45, we get 0 with a remainder of 18.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 18 and we're left with 18.
Take the next digit (8) from the dividend and append it to 18, then repeat: 188 / 45

Let's proceed to step 3:
188 divided by 45 is 4 with a remainder of 8.
The next digit of our result is 4. 
Result so far: 4.0
Deduct 180 from 188 and we're left with 8.
Grab the next digit (2) from the dividend, add it to 8, then carry on: 82 / 45

On to step 4:
The number 45 fits into 82 1 times, leaving a remainder of 37.
Put 1 as the next digit of the answer. 
Result so far: 41.0
Deduct 45 from 82 and we're left with 37.
Grab the next digit (1) from the dividend, add it to 37, then carry on: 371 / 45

On to step 5:
45 can be fit into 371 8 times, resulting in a remainder of 11.
Record the quotient 8 as the next digit in the result. 
Result so far: 418.0
If we subtract 360 from 371, we get 11.
Take the next digit (9) from the dividend and append it to 11, then repeat: 119 / 45

Going ahead to step 6:
The number 45 fits into 119 2 times, leaving a remainder of 29.
The number 2 becomes the next digit in our result. 
Result so far: 4182.0
If we subtract 90 from 119, we get 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 7:
290 divided by 45 is 6 with a remainder of 20.
Record the quotient 6 as the next digit in the result. 
Result so far: 4182.6
The remainder is 20 after subtracting 270 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Going ahead to step 8:
When dividing 200 by 45, we get 4 with a remainder of 20.
Write down 4 as next digit of the result. 
Result so far: 4182.64
Deduct 180 from 200 and we're left 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 9:
If we divide 200 by 45, we get 4 and a remainder of 20.
The number 4 becomes the next digit in our result. 
Result so far: 4182.644
Subtracting 180 from 200 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.

The final result is 4182.644 with a remainder of 0.002.