1092086 ÷ 289 
The aim is to understand the frequency of 289 in 1092086.

On to step 1:
When dividing 1 by 289, we get 0 with a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 289

Advancing to step 2:
When dividing 10 by 289, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Take the next digit (9) from the dividend and append it to 10, then repeat: 109 / 289

Going ahead to step 3:
109 divided by 289 is 0 with a remainder of 109.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 109 to get 109.
Include the next digit (2) from the dividend after 109, then repeat: 1092 / 289

Advancing to step 4:
When dividing 1092 by 289, we get 3 with a remainder of 225.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 867 from 1092, we get 225.
Take the next digit (0) from the dividend and append it to 225, then repeat: 2250 / 289

On to step 5:
289 goes into 2250 7 times with a remainder of 227.
Put 7 as the next digit of the answer. 
Result so far: 37.0
The remainder is 227 after subtracting 2023 from 2250.
Take the next digit (8) from the dividend and append it to 227, then repeat: 2278 / 289

Step 6:
289 can be fit into 2278 7 times, resulting in a remainder of 255.
The number 7 becomes the next digit in our result. 
Result so far: 377.0
If we subtract 2023 from 2278, we get 255.
Include the next digit (6) from the dividend after 255, then repeat: 2556 / 289

Going ahead to step 7:
289 goes into 2556 8 times with a remainder of 244.
The next digit of our result is 8. 
Result so far: 3778.0
Subtracting 2312 from 2556 leaves us with 244.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2440, and continue the process.

Let's proceed to step 8:
289 goes into 2440 8 times with a remainder of 128.
Record the quotient 8 as the next digit in the result. 
Result so far: 3778.8
If we subtract 2312 from 2440, we get 128.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1280, and continue the process.

Step 9:
When dividing 1280 by 289, we get 4 with a remainder of 124.
The next digit of our result is 4. 
Result so far: 3778.84
Deduct 1156 from 1280 and we're left with 124.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1240, and continue the process.

Advancing to step 10:
If we divide 1240 by 289, we get 4 and a remainder of 84.
Write down 4 as next digit of the result. 
Result so far: 3778.844
If we subtract 1156 from 1240, we get 84.
Since there are no more digits in the dividend, we add a zero to the remainder making it 840, and continue the process.

In conclusion, the division gives 3778.844 with a balance of 0.0084.