42940021 ÷ 137 
The aim is to understand the frequency of 137 in 42940021.

Advancing to step 1:
4 divided by 137 is 0 with a remainder of 4.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 4 to get 4.
Grab the next digit (2) from the dividend, add it to 4, then carry on: 42 / 137

Advancing to step 2:
If we divide 42 by 137, we get 0 and a remainder of 42.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 42, we end up with 42.
Include the next digit (9) from the dividend after 42, then repeat: 429 / 137

Let's proceed to step 3:
When dividing 429 by 137, we get 3 with a remainder of 18.
Put 3 as the next digit of the answer. 
Result so far: 3.0
If we subtract 411 from 429, we get 18.
Grab the next digit (4) from the dividend, add it to 18, then carry on: 184 / 137

Step 4:
137 can be fit into 184 1 times, resulting in a remainder of 47.
Use 1 as the next digit of our solution. 
Result so far: 31.0
Subtracting 137 from 184 leaves us with 47.
Grab the next digit (0) from the dividend, add it to 47, then carry on: 470 / 137

Let's proceed to step 5:
137 goes into 470 3 times with a remainder of 59.
Write down 3 as next digit of the result. 
Result so far: 313.0
The remainder is 59 after subtracting 411 from 470.
Grab the next digit (0) from the dividend, add it to 59, then carry on: 590 / 137

On to step 6:
The number 137 fits into 590 4 times, leaving a remainder of 42.
The number 4 becomes the next digit in our result. 
Result so far: 3134.0
The remainder is 42 after subtracting 548 from 590.
Fetch the next digit (2) from the dividend, attach it to 42 and continue: 422 / 137

Moving on to step 7:
422 divided by 137 is 3 with a remainder of 11.
Write down 3 as next digit of the result. 
Result so far: 31343.0
The remainder is 11 after subtracting 411 from 422.
Grab the next digit (1) from the dividend, add it to 11, then carry on: 111 / 137

Going ahead to step 8:
111 divided by 137 is 0 with a remainder of 111.
The number 0 becomes the next digit in our result. 
Result so far: 313430.0
The remainder is 111 after subtracting 0 from 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

Going ahead to step 9:
137 goes into 1110 8 times with a remainder of 14.
Write down 8 as next digit of the result. 
Result so far: 313430.8
Deduct 1096 from 1110 and we're left with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Moving on to step 10:
137 can be fit into 140 1 times, resulting in a remainder of 3.
Write down 1 as next digit of the result. 
Result so far: 313430.81
If we subtract 137 from 140, we get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 11:
The number 137 fits into 30 0 times, leaving a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 313430.81
Deduct 0 from 30 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Going ahead to step 12:
The number 137 fits into 300 2 times, leaving a remainder of 26.
The next digit of our result is 2. 
Result so far: 313430.8102
The remainder is 26 after subtracting 274 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 13:
137 goes into 260 1 times with a remainder of 123.
Write down 1 as next digit of the result. 
Result so far: 313430.81021
If we subtract 137 from 260, we get 123.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1230, and continue the process.

Step 14:
1230 divided by 137 is 8 with a remainder of 134.
Use 8 as the next digit of our solution. 
Result so far: 313430.810218
Subtracting 1096 from 1230 leaves us with 134.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1340, and continue the process.

Step 15:
1340 divided by 137 is 9 with a remainder of 107.
Put 9 as the next digit of the answer. 
Result so far: 313430.8102189
Subtract 1233 from 1340 to get 107.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1070, and continue the process.

Moving on to step 16:
137 can be fit into 1070 7 times, resulting in a remainder of 111.
The number 7 becomes the next digit in our result. 
Result so far: 313430.81021897
Subtract 959 from 1070 to get 111.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1110, and continue the process.

The final result is 313430.81021897 with a remainder of 1.11e-07.