91010713 divided by 81 
The aim is to understand the frequency of 81 in 91010713.

On to step 1:
9 divided by 81 is 0 with a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 9 to get 9.
Bring next digit (1) of the dividend behind the 9 and repeat the process: 91 / 81

Let's proceed to step 2:
If we divide 91 by 81, we get 1 and a remainder of 10.
The next digit of our result is 1. 
Result so far: 1.0
If we take 81 away from 91, we end up with 10.
Append the next digit (0) from the dividend to 10 and continue with: 100 / 81

Moving on to step 3:
81 can be fit into 100 1 times, resulting in a remainder of 19.
Write down 1 as next digit of the result. 
Result so far: 11.0
If we subtract 81 from 100, we get 19.
Take the next digit (1) from the dividend and append it to 19, then repeat: 191 / 81

Going ahead to step 4:
The number 81 fits into 191 2 times, leaving a remainder of 29.
Write down 2 as next digit of the result. 
Result so far: 112.0
Deduct 162 from 191 and we're left with 29.
Append the next digit (0) from the dividend to 29 and continue with: 290 / 81

Going ahead to step 5:
When dividing 290 by 81, we get 3 with a remainder of 47.
The next digit of our result is 3. 
Result so far: 1123.0
Subtracting 243 from 290 leaves us with 47.
Fetch the next digit (7) from the dividend, attach it to 47 and continue: 477 / 81

On to step 6:
The number 81 fits into 477 5 times, leaving a remainder of 72.
Record the quotient 5 as the next digit in the result. 
Result so far: 11235.0
If we take 405 away from 477, we end up with 72.
Bring next digit (1) of the dividend behind the 72 and repeat the process: 721 / 81

Step 7:
721 divided by 81 is 8 with a remainder of 73.
Put 8 as the next digit of the answer. 
Result so far: 112358.0
If we subtract 648 from 721, we get 73.
Take the next digit (3) from the dividend and append it to 73, then repeat: 733 / 81

On to step 8:
If we divide 733 by 81, we get 9 and a remainder of 4.
The next digit of our result is 9. 
Result so far: 1123589.0
The remainder is 4 after subtracting 729 from 733.
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:
The number 81 fits into 40 0 times, leaving a remainder of 40.
The next digit of our result is 0. 
Result so far: 1123589.0
The remainder is 40 after subtracting 0 from 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:
81 goes into 400 4 times with a remainder of 76.
The next digit of our result is 4. 
Result so far: 1123589.04
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.

Let's proceed to step 11:
81 goes into 760 9 times with a remainder of 31.
Write down 9 as next digit of the result. 
Result so far: 1123589.049
Subtracting 729 from 760 leaves us with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Advancing to step 12:
81 can be fit into 310 3 times, resulting in a remainder of 67.
The number 3 becomes the next digit in our result. 
Result so far: 1123589.0493
Subtracting 243 from 310 leaves us 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.

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: 1123589.04938
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.

Moving on to step 14:
81 can be fit into 220 2 times, resulting in a remainder of 58.
The number 2 becomes the next digit in our result. 
Result so far: 1123589.049382
If we subtract 162 from 220, we get 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Step 15:
The number 81 fits into 580 7 times, leaving a remainder of 13.
Put 7 as the next digit of the answer. 
Result so far: 1123589.0493827
Subtracting 567 from 580 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 16:
81 can be fit into 130 1 times, resulting in a remainder of 49.
Put 1 as the next digit of the answer. 
Result so far: 1123589.04938271
If we subtract 81 from 130, we get 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

The quotient of the division is 1123589.04938271, and the remainder is 4.9e-08.