We divide 38206 by 65
We want to divide 38206 by 65.

Step 1:
If we divide 3 by 65, we get 0 and a remainder of 3.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Append the next digit (8) from the dividend to 3 and continue with: 38 / 65

Let's proceed to step 2:
The number 65 fits into 38 0 times, leaving a remainder of 38.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 38, we get 38.
Append the next digit (2) from the dividend to 38 and continue with: 382 / 65

On to step 3:
65 goes into 382 5 times with a remainder of 57.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 325 away from 382, we end up with 57.
Fetch the next digit (0) from the dividend, attach it to 57 and continue: 570 / 65

Moving on to step 4:
65 goes into 570 8 times with a remainder of 50.
Use 8 as the next digit of our solution. 
Result so far: 58.0
The remainder is 50 after subtracting 520 from 570.
Append the next digit (6) from the dividend to 50 and continue with: 506 / 65

Step 5:
When dividing 506 by 65, we get 7 with a remainder of 51.
Use 7 as the next digit of our solution. 
Result so far: 587.0
Subtract 455 from 506 to get 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Step 6:
The number 65 fits into 510 7 times, leaving a remainder of 55.
Write down 7 as next digit of the result. 
Result so far: 587.7
Deduct 455 from 510 and we're left with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Moving on to step 7:
550 divided by 65 is 8 with a remainder of 30.
The next digit of our result is 8. 
Result so far: 587.78
Subtract 520 from 550 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 8:
65 goes into 300 4 times with a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 587.784
Deduct 260 from 300 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 9:
65 goes into 400 6 times with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 587.7846
Subtract 390 from 400 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 10:
65 can be fit into 100 1 times, resulting in a remainder of 35.
The next digit of our result is 1. 
Result so far: 587.78461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 11:
If we divide 350 by 65, we get 5 and a remainder of 25.
The number 5 becomes the next digit in our result. 
Result so far: 587.784615
Subtract 325 from 350 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 12:
65 goes into 250 3 times with a remainder of 55.
Write down 3 as next digit of the result. 
Result so far: 587.7846153
Subtracting 195 from 250 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 13:
The number 65 fits into 550 8 times, leaving a remainder of 30.
Use 8 as the next digit of our solution. 
Result so far: 587.78461538
Subtracting 520 from 550 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 587.78461538 with a balance of 3e-08.