10208397 ÷ 677 
Our goal is to divide 10208397 by 677.

Step 1:
If we divide 1 by 677, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 677

Step 2:
10 divided by 677 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Append the next digit (2) from the dividend to 10 and continue with: 102 / 677

Going ahead to step 3:
677 goes into 102 0 times with a remainder of 102.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 102, we get 102.
Include the next digit (0) from the dividend after 102, then repeat: 1020 / 677

Step 4:
677 goes into 1020 1 times with a remainder of 343.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 677 from 1020 leaves us with 343.
Include the next digit (8) from the dividend after 343, then repeat: 3438 / 677

On to step 5:
When dividing 3438 by 677, we get 5 with a remainder of 53.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
The remainder is 53 after subtracting 3385 from 3438.
Take the next digit (3) from the dividend and append it to 53, then repeat: 533 / 677

Advancing to step 6:
677 can be fit into 533 0 times, resulting in a remainder of 533.
Record the quotient 0 as the next digit in the result. 
Result so far: 150.0
The remainder is 533 after subtracting 0 from 533.
Fetch the next digit (9) from the dividend, attach it to 533 and continue: 5339 / 677

Step 7:
677 can be fit into 5339 7 times, resulting in a remainder of 600.
Use 7 as the next digit of our solution. 
Result so far: 1507.0
If we subtract 4739 from 5339, we get 600.
Append the next digit (7) from the dividend to 600 and continue with: 6007 / 677

Step 8:
677 can be fit into 6007 8 times, resulting in a remainder of 591.
Put 8 as the next digit of the answer. 
Result so far: 15078.0
The remainder is 591 after subtracting 5416 from 6007.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5910, and continue the process.

Step 9:
The number 677 fits into 5910 8 times, leaving a remainder of 494.
Record the quotient 8 as the next digit in the result. 
Result so far: 15078.8
The remainder is 494 after subtracting 5416 from 5910.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4940, and continue the process.

Moving on to step 10:
The number 677 fits into 4940 7 times, leaving a remainder of 201.
The next digit of our result is 7. 
Result so far: 15078.87
Subtract 4739 from 4940 to get 201.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2010, and continue the process.

Moving on to step 11:
When dividing 2010 by 677, we get 2 with a remainder of 656.
Write down 2 as next digit of the result. 
Result so far: 15078.872
Subtracting 1354 from 2010 leaves us with 656.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6560, and continue the process.

Going ahead to step 12:
The number 677 fits into 6560 9 times, leaving a remainder of 467.
Record the quotient 9 as the next digit in the result. 
Result so far: 15078.8729
If we subtract 6093 from 6560, we get 467.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4670, and continue the process.

Let's proceed to step 13:
677 can be fit into 4670 6 times, resulting in a remainder of 608.
The next digit of our result is 6. 
Result so far: 15078.87296
Deduct 4062 from 4670 and we're left with 608.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6080, and continue the process.

Step 14:
677 goes into 6080 8 times with a remainder of 664.
The number 8 becomes the next digit in our result. 
Result so far: 15078.872968
Subtract 5416 from 6080 to get 664.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6640, and continue the process.

Let's proceed to step 15:
677 goes into 6640 9 times with a remainder of 547.
Write down 9 as next digit of the result. 
Result so far: 15078.8729689
Subtracting 6093 from 6640 leaves us with 547.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5470, and continue the process.

Moving on to step 16:
677 goes into 5470 8 times with a remainder of 54.
The number 8 becomes the next digit in our result. 
Result so far: 15078.87296898
If we subtract 5416 from 5470, we get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

In conclusion, the division gives 15078.87296898 with a balance of 5.4e-08.