We look at the division of 642181 by 81 
We're looking to find how many times 81 goes into 642181.

Moving on to step 1:
81 goes into 6 0 times with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Bring next digit (4) of the dividend behind the 6 and repeat the process: 64 / 81

Step 2:
When dividing 64 by 81, we get 0 with a remainder of 64.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 64, we get 64.
Append the next digit (2) from the dividend to 64 and continue with: 642 / 81

On to step 3:
When dividing 642 by 81, we get 7 with a remainder of 75.
Write down 7 as next digit of the result. 
Result so far: 7.0
Subtracting 567 from 642 leaves us with 75.
Take the next digit (1) from the dividend and append it to 75, then repeat: 751 / 81

Step 4:
When dividing 751 by 81, we get 9 with a remainder of 22.
Write down 9 as next digit of the result. 
Result so far: 79.0
Subtracting 729 from 751 leaves us with 22.
Append the next digit (8) from the dividend to 22 and continue with: 228 / 81

Step 5:
81 goes into 228 2 times with a remainder of 66.
Record the quotient 2 as the next digit in the result. 
Result so far: 792.0
Subtract 162 from 228 to get 66.
Take the next digit (1) from the dividend and append it to 66, then repeat: 661 / 81

Moving on to step 6:
81 goes into 661 8 times with a remainder of 13.
Record the quotient 8 as the next digit in the result. 
Result so far: 7928.0
If we subtract 648 from 661, we get 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

On to step 7:
81 can be fit into 130 1 times, resulting in a remainder of 49.
Write down 1 as next digit of the result. 
Result so far: 7928.1
If we take 81 away from 130, we end up with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Let's proceed to step 8:
If we divide 490 by 81, we get 6 and a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 7928.16
The remainder is 4 after subtracting 486 from 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Step 9:
If we divide 40 by 81, we get 0 and a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 7928.16
Subtract 0 from 40 to get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 10:
If we divide 400 by 81, we get 4 and a remainder of 76.
The next digit of our result is 4. 
Result so far: 7928.1604
The remainder is 76 after subtracting 324 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 11:
760 divided by 81 is 9 with a remainder of 31.
Put 9 as the next digit of the answer. 
Result so far: 7928.16049
If we subtract 729 from 760, 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.

Step 12:
81 goes into 310 3 times with a remainder of 67.
Write down 3 as next digit of the result. 
Result so far: 7928.160493
Deduct 243 from 310 and we're left with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 13:
When dividing 670 by 81, we get 8 with a remainder of 22.
The next digit of our result is 8. 
Result so far: 7928.1604938
The remainder is 22 after subtracting 648 from 670.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 14:
When dividing 220 by 81, we get 2 with a remainder of 58.
The next digit of our result is 2. 
Result so far: 7928.16049382
If we take 162 away from 220, we end up with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

After the division, we end up with 7928.16049382 and a remainder of 5.8e-08.