627630 ÷ 17 
Our goal is to divide 627630 by 17.

Let's proceed to step 1:
If we divide 6 by 17, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (2) from the dividend to 6 and continue with: 62 / 17

Step 2:
17 can be fit into 62 3 times, resulting in a remainder of 11.
The next digit of our result is 3. 
Result so far: 3.0
The remainder is 11 after subtracting 51 from 62.
Take the next digit (7) from the dividend and append it to 11, then repeat: 117 / 17

Let's proceed to step 3:
117 divided by 17 is 6 with a remainder of 15.
Use 6 as the next digit of our solution. 
Result so far: 36.0
If we take 102 away from 117, we end up with 15.
Include the next digit (6) from the dividend after 15, then repeat: 156 / 17

Moving on to step 4:
17 can be fit into 156 9 times, resulting in a remainder of 3.
Write down 9 as next digit of the result. 
Result so far: 369.0
If we subtract 153 from 156, we get 3.
Bring next digit (3) of the dividend behind the 3 and repeat the process: 33 / 17

On to step 5:
33 divided by 17 is 1 with a remainder of 16.
The number 1 becomes the next digit in our result. 
Result so far: 3691.0
Subtract 17 from 33 to get 16.
Append the next digit (0) from the dividend to 16 and continue with: 160 / 17

Moving on to step 6:
17 can be fit into 160 9 times, resulting in a remainder of 7.
The next digit of our result is 9. 
Result so far: 36919.0
Deduct 153 from 160 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 7:
17 goes into 70 4 times with a remainder of 2.
The number 4 becomes the next digit in our result. 
Result so far: 36919.4
Subtracting 68 from 70 leaves us 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.

On to step 8:
If we divide 20 by 17, we get 1 and a remainder of 3.
The next digit of our result is 1. 
Result so far: 36919.41
Subtract 17 from 20 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 9:
When dividing 30 by 17, we get 1 with a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 36919.411
If we take 17 away from 30, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 36919.411 with a balance of 0.0013.