We look at the division of 638626 by 97 
Let's see how many times 97 fits into 638626.

Advancing to step 1:
If we divide 6 by 97, we get 0 and a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Grab the next digit (3) from the dividend, add it to 6, then carry on: 63 / 97

Step 2:
If we divide 63 by 97, we get 0 and a remainder of 63.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we take 0 away from 63, we end up with 63.
Take the next digit (8) from the dividend and append it to 63, then repeat: 638 / 97

Step 3:
638 divided by 97 is 6 with a remainder of 56.
Use 6 as the next digit of our solution. 
Result so far: 6.0
The remainder is 56 after subtracting 582 from 638.
Include the next digit (6) from the dividend after 56, then repeat: 566 / 97

On to step 4:
97 goes into 566 5 times with a remainder of 81.
The next digit of our result is 5. 
Result so far: 65.0
Deduct 485 from 566 and we're left with 81.
Include the next digit (2) from the dividend after 81, then repeat: 812 / 97

Step 5:
97 can be fit into 812 8 times, resulting in a remainder of 36.
Write down 8 as next digit of the result. 
Result so far: 658.0
Subtract 776 from 812 to get 36.
Fetch the next digit (6) from the dividend, attach it to 36 and continue: 366 / 97

Moving on to step 6:
97 can be fit into 366 3 times, resulting in a remainder of 75.
Record the quotient 3 as the next digit in the result. 
Result so far: 6583.0
Subtracting 291 from 366 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Let's proceed to step 7:
97 goes into 750 7 times with a remainder of 71.
The number 7 becomes the next digit in our result. 
Result so far: 6583.7
The remainder is 71 after subtracting 679 from 750.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Let's proceed to step 8:
When dividing 710 by 97, we get 7 with a remainder of 31.
Put 7 as the next digit of the answer. 
Result so far: 6583.77
If we subtract 679 from 710, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

After the division, we end up with 6583.77 and a remainder of 0.031.