We divide 9565 by 19
We want to figure out the number of times 9565 can be divided by 19.

Going ahead to step 1:
19 goes into 9 0 times with a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 9 and we're left with 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 19

Moving on to step 2:
95 divided by 19 is 5 with a remainder of 0.
The next digit of our result is 5. 
Result so far: 5.0
Deduct 95 from 95 and we're left with 0.
Append the next digit (6) from the dividend to 0 and continue with: 6 / 19

On to step 3:
19 goes into 6 0 times with a remainder of 6.
Use 0 as the next digit of our solution. 
Result so far: 50.0
Subtracting 0 from 6 leaves us with 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 19

Advancing to step 4:
The number 19 fits into 65 3 times, leaving a remainder of 8.
Use 3 as the next digit of our solution. 
Result so far: 503.0
If we subtract 57 from 65, we get 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 5:
19 goes into 80 4 times with a remainder of 4.
The next digit of our result is 4. 
Result so far: 503.4
Deduct 76 from 80 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 6:
19 goes into 40 2 times with a remainder of 2.
The next digit of our result is 2. 
Result so far: 503.42
If we take 38 away from 40, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 7:
19 can be fit into 20 1 times, resulting in a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 503.421
The remainder is 1 after subtracting 19 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 8:
19 goes into 10 0 times with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 503.421
Subtracting 0 from 10 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 9:
When dividing 100 by 19, we get 5 with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 503.42105
The remainder is 5 after subtracting 95 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Advancing to step 10:
If we divide 50 by 19, we get 2 and a remainder of 12.
The number 2 becomes the next digit in our result. 
Result so far: 503.421052
The remainder is 12 after subtracting 38 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Moving on to step 11:
120 divided by 19 is 6 with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 503.4210526
If we subtract 114 from 120, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Moving on to step 12:
19 goes into 60 3 times with a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 503.42105263
The remainder is 3 after subtracting 57 from 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

In conclusion, the division gives 503.42105263 with a balance of 3e-09.