101586 ÷ 98 
The aim is to understand the frequency of 98 in 101586.

Moving on to step 1:
When dividing 1 by 98, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 98

Going ahead to step 2:
If we divide 10 by 98, we get 0 and a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 10 leaves us with 10.
Grab the next digit (1) from the dividend, add it to 10, then carry on: 101 / 98

Advancing to step 3:
101 divided by 98 is 1 with a remainder of 3.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 98 from 101 leaves us with 3.
Append the next digit (5) from the dividend to 3 and continue with: 35 / 98

Advancing to step 4:
98 can be fit into 35 0 times, resulting in a remainder of 35.
The number 0 becomes the next digit in our result. 
Result so far: 10.0
If we take 0 away from 35, we end up with 35.
Bring next digit (8) of the dividend behind the 35 and repeat the process: 358 / 98

Going ahead to step 5:
The number 98 fits into 358 3 times, leaving a remainder of 64.
Use 3 as the next digit of our solution. 
Result so far: 103.0
The remainder is 64 after subtracting 294 from 358.
Take the next digit (6) from the dividend and append it to 64, then repeat: 646 / 98

Going ahead to step 6:
When dividing 646 by 98, we get 6 with a remainder of 58.
Use 6 as the next digit of our solution. 
Result so far: 1036.0
Deduct 588 from 646 and we're left with 58.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

Let's proceed to step 7:
When dividing 580 by 98, we get 5 with a remainder of 90.
Write down 5 as next digit of the result. 
Result so far: 1036.5
Subtracting 490 from 580 leaves us with 90.
Since there are no more digits in the dividend, we add a zero to the remainder making it 900, and continue the process.

Going ahead to step 8:
900 divided by 98 is 9 with a remainder of 18.
The next digit of our result is 9. 
Result so far: 1036.59
If we take 882 away from 900, we end up with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Advancing to step 9:
The number 98 fits into 180 1 times, leaving a remainder of 82.
The number 1 becomes the next digit in our result. 
Result so far: 1036.591
Deduct 98 from 180 and we're left with 82.
Since there are no more digits in the dividend, we add a zero to the remainder making it 820, and continue the process.

Let's proceed to step 10:
98 goes into 820 8 times with a remainder of 36.
Use 8 as the next digit of our solution. 
Result so far: 1036.5918
Subtracting 784 from 820 leaves us with 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 11:
98 can be fit into 360 3 times, resulting in a remainder of 66.
Write down 3 as next digit of the result. 
Result so far: 1036.59183
The remainder is 66 after subtracting 294 from 360.
Since there are no more digits in the dividend, we add a zero to the remainder making it 660, and continue the process.

Step 12:
The number 98 fits into 660 6 times, leaving a remainder of 72.
The number 6 becomes the next digit in our result. 
Result so far: 1036.591836
Subtract 588 from 660 to get 72.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

On to step 13:
98 goes into 720 7 times with a remainder of 34.
Record the quotient 7 as the next digit in the result. 
Result so far: 1036.5918367
Subtract 686 from 720 to get 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

Let's proceed to step 14:
98 can be fit into 340 3 times, resulting in a remainder of 46.
Use 3 as the next digit of our solution. 
Result so far: 1036.59183673
If we subtract 294 from 340, we get 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

In conclusion, the division gives 1036.59183673 with a balance of 4.6e-08.