We look at the division of 19681 by 45 
Our goal is to divide 19681 by 45.

Let's proceed to step 1:
1 divided by 45 is 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (9) from the dividend and append it to 1, then repeat: 19 / 45

Going ahead to step 2:
If we divide 19 by 45, we get 0 and a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 19 leaves us with 19.
Take the next digit (6) from the dividend and append it to 19, then repeat: 196 / 45

Step 3:
45 goes into 196 4 times with a remainder of 16.
The next digit of our result is 4. 
Result so far: 4.0
If we take 180 away from 196, we end up with 16.
Append the next digit (8) from the dividend to 16 and continue with: 168 / 45

On to step 4:
The number 45 fits into 168 3 times, leaving a remainder of 33.
Record the quotient 3 as the next digit in the result. 
Result so far: 43.0
If we take 135 away from 168, we end up with 33.
Fetch the next digit (1) from the dividend, attach it to 33 and continue: 331 / 45

Step 5:
45 can be fit into 331 7 times, resulting in a remainder of 16.
Put 7 as the next digit of the answer. 
Result so far: 437.0
Deduct 315 from 331 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 6:
45 goes into 160 3 times with a remainder of 25.
Record the quotient 3 as the next digit in the result. 
Result so far: 437.3
Subtract 135 from 160 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Moving on to step 7:
250 divided by 45 is 5 with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 437.35
If we subtract 225 from 250, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
If we divide 250 by 45, we get 5 and a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 437.355
If we take 225 away from 250, we end up with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 437.355 with a balance of 0.0025.