We're dividing 110138 by 71 
The aim is to understand the frequency of 71 in 110138.

Let's proceed to step 1:
The number 71 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Grab the next digit (1) from the dividend, add it to 1, then carry on: 11 / 71

Advancing to step 2:
If we divide 11 by 71, we get 0 and a remainder of 11.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 11 after subtracting 0 from 11.
Fetch the next digit (0) from the dividend, attach it to 11 and continue: 110 / 71

Advancing to step 3:
71 can be fit into 110 1 times, resulting in a remainder of 39.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
If we subtract 71 from 110, we get 39.
Fetch the next digit (1) from the dividend, attach it to 39 and continue: 391 / 71

Step 4:
391 divided by 71 is 5 with a remainder of 36.
The number 5 becomes the next digit in our result. 
Result so far: 15.0
If we take 355 away from 391, we end up with 36.
Include the next digit (3) from the dividend after 36, then repeat: 363 / 71

Going ahead to step 5:
71 goes into 363 5 times with a remainder of 8.
Record the quotient 5 as the next digit in the result. 
Result so far: 155.0
Subtracting 355 from 363 leaves us with 8.
Take the next digit (8) from the dividend and append it to 8, then repeat: 88 / 71

Going ahead to step 6:
If we divide 88 by 71, we get 1 and a remainder of 17.
The next digit of our result is 1. 
Result so far: 1551.0
If we take 71 away from 88, we end up with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Moving on to step 7:
170 divided by 71 is 2 with a remainder of 28.
The next digit of our result is 2. 
Result so far: 1551.2
Deduct 142 from 170 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

On to step 8:
280 divided by 71 is 3 with a remainder of 67.
Put 3 as the next digit of the answer. 
Result so far: 1551.23
Subtract 213 from 280 to get 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Step 9:
The number 71 fits into 670 9 times, leaving a remainder of 31.
The next digit of our result is 9. 
Result so far: 1551.239
Subtract 639 from 670 to get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Let's proceed to step 10:
The number 71 fits into 310 4 times, leaving a remainder of 26.
Record the quotient 4 as the next digit in the result. 
Result so far: 1551.2394
If we subtract 284 from 310, we get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Advancing to step 11:
260 divided by 71 is 3 with a remainder of 47.
Use 3 as the next digit of our solution. 
Result so far: 1551.23943
Subtract 213 from 260 to get 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Step 12:
The number 71 fits into 470 6 times, leaving a remainder of 44.
Put 6 as the next digit of the answer. 
Result so far: 1551.239436
If we take 426 away from 470, we end up with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 13:
440 divided by 71 is 6 with a remainder of 14.
The number 6 becomes the next digit in our result. 
Result so far: 1551.2394366
The remainder is 14 after subtracting 426 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

In conclusion, the division gives 1551.2394366 with a balance of 1.4e-07.