10529358 ÷ 509 
The aim is to understand the frequency of 509 in 10529358.

Let's proceed to step 1:
If we divide 1 by 509, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 509

Advancing to step 2:
10 divided by 509 is 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Grab the next digit (5) from the dividend, add it to 10, then carry on: 105 / 509

Moving on to step 3:
105 divided by 509 is 0 with a remainder of 105.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 105 leaves us with 105.
Grab the next digit (2) from the dividend, add it to 105, then carry on: 1052 / 509

Let's proceed to step 4:
If we divide 1052 by 509, we get 2 and a remainder of 34.
Record the quotient 2 as the next digit in the result. 
Result so far: 2.0
If we take 1018 away from 1052, we end up with 34.
Take the next digit (9) from the dividend and append it to 34, then repeat: 349 / 509

Moving on to step 5:
509 can be fit into 349 0 times, resulting in a remainder of 349.
Put 0 as the next digit of the answer. 
Result so far: 20.0
Subtracting 0 from 349 leaves us with 349.
Include the next digit (3) from the dividend after 349, then repeat: 3493 / 509

Advancing to step 6:
3493 divided by 509 is 6 with a remainder of 439.
Use 6 as the next digit of our solution. 
Result so far: 206.0
Subtracting 3054 from 3493 leaves us with 439.
Bring next digit (5) of the dividend behind the 439 and repeat the process: 4395 / 509

Going ahead to step 7:
509 can be fit into 4395 8 times, resulting in a remainder of 323.
The next digit of our result is 8. 
Result so far: 2068.0
Deduct 4072 from 4395 and we're left with 323.
Bring next digit (8) of the dividend behind the 323 and repeat the process: 3238 / 509

Let's proceed to step 8:
The number 509 fits into 3238 6 times, leaving a remainder of 184.
Write down 6 as next digit of the result. 
Result so far: 20686.0
Subtract 3054 from 3238 to get 184.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1840, and continue the process.

Step 9:
1840 divided by 509 is 3 with a remainder of 313.
The number 3 becomes the next digit in our result. 
Result so far: 20686.3
Deduct 1527 from 1840 and we're left with 313.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3130, and continue the process.

On to step 10:
3130 divided by 509 is 6 with a remainder of 76.
The next digit of our result is 6. 
Result so far: 20686.36
The remainder is 76 after subtracting 3054 from 3130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Advancing to step 11:
509 goes into 760 1 times with a remainder of 251.
Record the quotient 1 as the next digit in the result. 
Result so far: 20686.361
If we take 509 away from 760, we end up with 251.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2510, and continue the process.

On to step 12:
509 can be fit into 2510 4 times, resulting in a remainder of 474.
Use 4 as the next digit of our solution. 
Result so far: 20686.3614
Deduct 2036 from 2510 and we're left with 474.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4740, and continue the process.

On to step 13:
509 can be fit into 4740 9 times, resulting in a remainder of 159.
Use 9 as the next digit of our solution. 
Result so far: 20686.36149
If we take 4581 away from 4740, we end up 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.

Let's proceed to step 14:
If we divide 1590 by 509, we get 3 and a remainder of 63.
Put 3 as the next digit of the answer. 
Result so far: 20686.361493
Subtract 1527 from 1590 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Going ahead to step 15:
509 can be fit into 630 1 times, resulting in a remainder of 121.
Record the quotient 1 as the next digit in the result. 
Result so far: 20686.3614931
Subtracting 509 from 630 leaves us with 121.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1210, and continue the process.

Step 16:
If we divide 1210 by 509, we get 2 and a remainder of 192.
Write down 2 as next digit of the result. 
Result so far: 20686.36149312
If we subtract 1018 from 1210, we get 192.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1920, and continue the process.

In conclusion, the division gives 20686.36149312 with a balance of 1.92e-07.