We look at the division of 681666 by 97 
We're looking to find how many times 97 goes into 681666.

Step 1:
6 divided by 97 is 0 with a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 6, we get 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 97

Going ahead to step 2:
If we divide 68 by 97, we get 0 and a remainder of 68.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 68 after subtracting 0 from 68.
Bring next digit (1) of the dividend behind the 68 and repeat the process: 681 / 97

Moving on to step 3:
The number 97 fits into 681 7 times, leaving a remainder of 2.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
Subtract 679 from 681 to get 2.
Bring next digit (6) of the dividend behind the 2 and repeat the process: 26 / 97

Advancing to step 4:
97 can be fit into 26 0 times, resulting in a remainder of 26.
Put 0 as the next digit of the answer. 
Result so far: 70.0
If we take 0 away from 26, we end up with 26.
Fetch the next digit (6) from the dividend, attach it to 26 and continue: 266 / 97

On to step 5:
97 goes into 266 2 times with a remainder of 72.
Use 2 as the next digit of our solution. 
Result so far: 702.0
If we subtract 194 from 266, we get 72.
Append the next digit (6) from the dividend to 72 and continue with: 726 / 97

On to step 6:
97 can be fit into 726 7 times, resulting in a remainder of 47.
Record the quotient 7 as the next digit in the result. 
Result so far: 7027.0
Deduct 679 from 726 and we're left with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

On to step 7:
97 can be fit into 470 4 times, resulting in a remainder of 82.
The next digit of our result is 4. 
Result so far: 7027.4
The remainder is 82 after subtracting 388 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Moving on to step 8:
820 divided by 97 is 8 with a remainder of 44.
The number 8 becomes the next digit in our result. 
Result so far: 7027.48
Deduct 776 from 820 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 9:
The number 97 fits into 440 4 times, leaving a remainder of 52.
Write down 4 as next digit of the result. 
Result so far: 7027.484
Subtracting 388 from 440 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Step 10:
97 goes into 520 5 times with a remainder of 35.
The next digit of our result is 5. 
Result so far: 7027.4845
If we subtract 485 from 520, we 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.

On to step 11:
If we divide 350 by 97, we get 3 and a remainder of 59.
The next digit of our result is 3. 
Result so far: 7027.48453
The remainder is 59 after subtracting 291 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Going ahead to step 12:
97 goes into 590 6 times with a remainder of 8.
Write down 6 as next digit of the result. 
Result so far: 7027.484536
Subtract 582 from 590 to 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 13:
The number 97 fits into 80 0 times, leaving a remainder of 80.
The next digit of our result is 0. 
Result so far: 7027.484536
If we subtract 0 from 80, we get 80.
Since there are no more digits in the dividend, we add a zero to the remainder making it 800, and continue the process.

Advancing to step 14:
97 can be fit into 800 8 times, resulting in a remainder of 24.
The number 8 becomes the next digit in our result. 
Result so far: 7027.48453608
The remainder is 24 after subtracting 776 from 800.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

After the division, we end up with 7027.48453608 and a remainder of 2.4e-08.