5809299 ÷ 509 
The aim is to understand the frequency of 509 in 5809299.

Step 1:
The number 509 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Take the next digit (8) from the dividend and append it to 5, then repeat: 58 / 509

Going ahead to step 2:
58 divided by 509 is 0 with a remainder of 58.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 58 and we're left with 58.
Append the next digit (0) from the dividend to 58 and continue with: 580 / 509

Moving on to step 3:
When dividing 580 by 509, we get 1 with a remainder of 71.
The next digit of our result is 1. 
Result so far: 1.0
Subtracting 509 from 580 leaves us with 71.
Bring next digit (9) of the dividend behind the 71 and repeat the process: 719 / 509

On to step 4:
If we divide 719 by 509, we get 1 and a remainder of 210.
The number 1 becomes the next digit in our result. 
Result so far: 11.0
If we take 509 away from 719, we end up with 210.
Fetch the next digit (2) from the dividend, attach it to 210 and continue: 2102 / 509

Step 5:
When dividing 2102 by 509, we get 4 with a remainder of 66.
The number 4 becomes the next digit in our result. 
Result so far: 114.0
Subtract 2036 from 2102 to get 66.
Include the next digit (9) from the dividend after 66, then repeat: 669 / 509

Let's proceed to step 6:
509 goes into 669 1 times with a remainder of 160.
Use 1 as the next digit of our solution. 
Result so far: 1141.0
The remainder is 160 after subtracting 509 from 669.
Grab the next digit (9) from the dividend, add it to 160, then carry on: 1609 / 509

Advancing to step 7:
When dividing 1609 by 509, we get 3 with a remainder of 82.
Use 3 as the next digit of our solution. 
Result so far: 11413.0
The remainder is 82 after subtracting 1527 from 1609.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Moving on to step 8:
509 can be fit into 820 1 times, resulting in a remainder of 311.
Use 1 as the next digit of our solution. 
Result so far: 11413.1
The remainder is 311 after subtracting 509 from 820.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3110, and continue the process.

Advancing to step 9:
When dividing 3110 by 509, we get 6 with a remainder of 56.
Use 6 as the next digit of our solution. 
Result so far: 11413.16
The remainder is 56 after subtracting 3054 from 3110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Advancing to step 10:
If we divide 560 by 509, we get 1 and a remainder of 51.
Put 1 as the next digit of the answer. 
Result so far: 11413.161
Subtracting 509 from 560 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 11:
The number 509 fits into 510 1 times, leaving a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 11413.1611
If we subtract 509 from 510, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The final result is 11413.1611 with a remainder of 1e-05.