90965805 ÷ 513 
The aim is to understand the frequency of 513 in 90965805.

Step 1:
513 goes into 9 0 times with a remainder of 9.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Grab the next digit (0) from the dividend, add it to 9, then carry on: 90 / 513

Let's proceed to step 2:
If we divide 90 by 513, we get 0 and a remainder of 90.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 90 after subtracting 0 from 90.
Append the next digit (9) from the dividend to 90 and continue with: 909 / 513

Going ahead to step 3:
513 goes into 909 1 times with a remainder of 396.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 513 from 909 to get 396.
Append the next digit (6) from the dividend to 396 and continue with: 3966 / 513

On to step 4:
513 can be fit into 3966 7 times, resulting in a remainder of 375.
Record the quotient 7 as the next digit in the result. 
Result so far: 17.0
Deduct 3591 from 3966 and we're left with 375.
Append the next digit (5) from the dividend to 375 and continue with: 3755 / 513

Let's proceed to step 5:
If we divide 3755 by 513, we get 7 and a remainder of 164.
The next digit of our result is 7. 
Result so far: 177.0
If we take 3591 away from 3755, we end up with 164.
Include the next digit (8) from the dividend after 164, then repeat: 1648 / 513

Step 6:
The number 513 fits into 1648 3 times, leaving a remainder of 109.
Record the quotient 3 as the next digit in the result. 
Result so far: 1773.0
If we take 1539 away from 1648, we end up with 109.
Include the next digit (0) from the dividend after 109, then repeat: 1090 / 513

Step 7:
When dividing 1090 by 513, we get 2 with a remainder of 64.
The next digit of our result is 2. 
Result so far: 17732.0
The remainder is 64 after subtracting 1026 from 1090.
Take the next digit (5) from the dividend and append it to 64, then repeat: 645 / 513

Moving on to step 8:
The number 513 fits into 645 1 times, leaving a remainder of 132.
Record the quotient 1 as the next digit in the result. 
Result so far: 177321.0
The remainder is 132 after subtracting 513 from 645.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1320, and continue the process.

Going ahead to step 9:
513 can be fit into 1320 2 times, resulting in a remainder of 294.
Put 2 as the next digit of the answer. 
Result so far: 177321.2
Deduct 1026 from 1320 and we're left with 294.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2940, and continue the process.

Advancing to step 10:
If we divide 2940 by 513, we get 5 and a remainder of 375.
Record the quotient 5 as the next digit in the result. 
Result so far: 177321.25
If we subtract 2565 from 2940, we get 375.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3750, and continue the process.

On to step 11:
3750 divided by 513 is 7 with a remainder of 159.
The number 7 becomes the next digit in our result. 
Result so far: 177321.257
Subtracting 3591 from 3750 leaves us with 159.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1590, and continue the process.

Moving on to step 12:
513 goes into 1590 3 times with a remainder of 51.
Record the quotient 3 as the next digit in the result. 
Result so far: 177321.2573
Subtracting 1539 from 1590 leaves us with 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Let's proceed to step 13:
The number 513 fits into 510 0 times, leaving a remainder of 510.
Put 0 as the next digit of the answer. 
Result so far: 177321.2573
If we subtract 0 from 510, we get 510.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5100, and continue the process.

Advancing to step 14:
513 can be fit into 5100 9 times, resulting in a remainder of 483.
Write down 9 as next digit of the result. 
Result so far: 177321.257309
If we subtract 4617 from 5100, we get 483.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4830, and continue the process.

Moving on to step 15:
If we divide 4830 by 513, we get 9 and a remainder of 213.
Write down 9 as next digit of the result. 
Result so far: 177321.2573099
If we subtract 4617 from 4830, we get 213.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2130, and continue the process.

The final result is 177321.2573099 with a remainder of 2.13e-06.