We look at the division of 637142 by 81 
We want to divide 637142 by 81.

Step 1:
When dividing 6 by 81, we get 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Fetch the next digit (3) from the dividend, attach it to 6 and continue: 63 / 81

Moving on to step 2:
63 divided by 81 is 0 with a remainder of 63.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 63 after subtracting 0 from 63.
Bring next digit (7) of the dividend behind the 63 and repeat the process: 637 / 81

On to step 3:
637 divided by 81 is 7 with a remainder of 70.
Write down 7 as next digit of the result. 
Result so far: 7.0
The remainder is 70 after subtracting 567 from 637.
Fetch the next digit (1) from the dividend, attach it to 70 and continue: 701 / 81

Advancing to step 4:
The number 81 fits into 701 8 times, leaving a remainder of 53.
Record the quotient 8 as the next digit in the result. 
Result so far: 78.0
The remainder is 53 after subtracting 648 from 701.
Grab the next digit (4) from the dividend, add it to 53, then carry on: 534 / 81

On to step 5:
534 divided by 81 is 6 with a remainder of 48.
Use 6 as the next digit of our solution. 
Result so far: 786.0
The remainder is 48 after subtracting 486 from 534.
Fetch the next digit (2) from the dividend, attach it to 48 and continue: 482 / 81

On to step 6:
81 can be fit into 482 5 times, resulting in a remainder of 77.
Record the quotient 5 as the next digit in the result. 
Result so far: 7865.0
If we take 405 away from 482, we end up with 77.
Since there are no more digits in the dividend, we add a zero to the remainder making it 770, and continue the process.

Moving on to step 7:
81 can be fit into 770 9 times, resulting in a remainder of 41.
Record the quotient 9 as the next digit in the result. 
Result so far: 7865.9
Subtracting 729 from 770 leaves us with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Let's proceed to step 8:
If we divide 410 by 81, we get 5 and a remainder of 5.
The number 5 becomes the next digit in our result. 
Result so far: 7865.95
If we take 405 away from 410, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

On to step 9:
81 can be fit into 50 0 times, resulting in a remainder of 50.
The number 0 becomes the next digit in our result. 
Result so far: 7865.95
Subtract 0 from 50 to get 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Let's proceed to step 10:
81 can be fit into 500 6 times, resulting in a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 7865.9506
Subtract 486 from 500 to get 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 11:
81 goes into 140 1 times with a remainder of 59.
Put 1 as the next digit of the answer. 
Result so far: 7865.95061
The remainder is 59 after subtracting 81 from 140.
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:
590 divided by 81 is 7 with a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 7865.950617
The remainder is 23 after subtracting 567 from 590.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Going ahead to step 13:
The number 81 fits into 230 2 times, leaving a remainder of 68.
Use 2 as the next digit of our solution. 
Result so far: 7865.9506172
If we subtract 162 from 230, we get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Moving on to step 14:
If we divide 680 by 81, we get 8 and a remainder of 32.
Put 8 as the next digit of the answer. 
Result so far: 7865.95061728
If we subtract 648 from 680, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

The final outcome is 7865.95061728, with a leftover of 3.2e-08.