877213 ÷ 97 
The aim is to understand the frequency of 97 in 877213.

Step 1:
97 goes into 8 0 times with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Take the next digit (7) from the dividend and append it to 8, then repeat: 87 / 97

Step 2:
When dividing 87 by 97, we get 0 with a remainder of 87.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 87 after subtracting 0 from 87.
Bring next digit (7) of the dividend behind the 87 and repeat the process: 877 / 97

Let's proceed to step 3:
97 goes into 877 9 times with a remainder of 4.
Write down 9 as next digit of the result. 
Result so far: 9.0
The remainder is 4 after subtracting 873 from 877.
Fetch the next digit (2) from the dividend, attach it to 4 and continue: 42 / 97

Advancing to step 4:
When dividing 42 by 97, we get 0 with a remainder of 42.
Write down 0 as next digit of the result. 
Result so far: 90.0
Subtracting 0 from 42 leaves us with 42.
Include the next digit (1) from the dividend after 42, then repeat: 421 / 97

Moving on to step 5:
421 divided by 97 is 4 with a remainder of 33.
Record the quotient 4 as the next digit in the result. 
Result so far: 904.0
If we subtract 388 from 421, we get 33.
Grab the next digit (3) from the dividend, add it to 33, then carry on: 333 / 97

Let's proceed to step 6:
97 goes into 333 3 times with a remainder of 42.
The number 3 becomes the next digit in our result. 
Result so far: 9043.0
If we subtract 291 from 333, we get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Advancing to step 7:
The number 97 fits into 420 4 times, leaving a remainder of 32.
The number 4 becomes the next digit in our result. 
Result so far: 9043.4
If we take 388 away from 420, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 8:
97 can be fit into 320 3 times, resulting in a remainder of 29.
Write down 3 as next digit of the result. 
Result so far: 9043.43
Subtracting 291 from 320 leaves us with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Moving on to step 9:
97 can be fit into 290 2 times, resulting in a remainder of 96.
Put 2 as the next digit of the answer. 
Result so far: 9043.432
The remainder is 96 after subtracting 194 from 290.
Since there are no more digits in the dividend, we add a zero to the remainder making it 960, and continue the process.

Advancing to step 10:
97 goes into 960 9 times with a remainder of 87.
The number 9 becomes the next digit in our result. 
Result so far: 9043.4329
Subtracting 873 from 960 leaves us with 87.
Since there are no more digits in the dividend, we add a zero to the remainder making it 870, and continue the process.

Going ahead to step 11:
The number 97 fits into 870 8 times, leaving a remainder of 94.
Put 8 as the next digit of the answer. 
Result so far: 9043.43298
If we take 776 away from 870, we end up with 94.
Since there are no more digits in the dividend, we add a zero to the remainder making it 940, and continue the process.

On to step 12:
97 can be fit into 940 9 times, resulting in a remainder of 67.
Put 9 as the next digit of the answer. 
Result so far: 9043.432989
Subtract 873 from 940 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.

Let's proceed to step 13:
The number 97 fits into 670 6 times, leaving a remainder of 88.
The number 6 becomes the next digit in our result. 
Result so far: 9043.4329896
The remainder is 88 after subtracting 582 from 670.
Since there are no more digits in the dividend, we add a zero to the remainder making it 880, and continue the process.

Advancing to step 14:
If we divide 880 by 97, we get 9 and a remainder of 7.
The next digit of our result is 9. 
Result so far: 9043.43298969
Deduct 873 from 880 and we're left with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Our division results in 9043.43298969 with a remaining 7e-09.