129977 ÷ 77 
The aim is to understand the frequency of 77 in 129977.

Let's proceed to step 1:
If we divide 1 by 77, we get 0 and a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 77

Step 2:
12 divided by 77 is 0 with a remainder of 12.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 12 after subtracting 0 from 12.
Take the next digit (9) from the dividend and append it to 12, then repeat: 129 / 77

Moving on to step 3:
The number 77 fits into 129 1 times, leaving a remainder of 52.
Use 1 as the next digit of our solution. 
Result so far: 1.0
Subtracting 77 from 129 leaves us with 52.
Take the next digit (9) from the dividend and append it to 52, then repeat: 529 / 77

Moving on to step 4:
77 can be fit into 529 6 times, resulting in a remainder of 67.
Write down 6 as next digit of the result. 
Result so far: 16.0
Subtracting 462 from 529 leaves us with 67.
Grab the next digit (7) from the dividend, add it to 67, then carry on: 677 / 77

Advancing to step 5:
The number 77 fits into 677 8 times, leaving a remainder of 61.
Record the quotient 8 as the next digit in the result. 
Result so far: 168.0
Deduct 616 from 677 and we're left with 61.
Append the next digit (7) from the dividend to 61 and continue with: 617 / 77

Step 6:
77 can be fit into 617 8 times, resulting in a remainder of 1.
Record the quotient 8 as the next digit in the result. 
Result so far: 1688.0
If we take 616 away from 617, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 7:
When dividing 10 by 77, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 1688.0
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 8:
When dividing 100 by 77, we get 1 with a remainder of 23.
The number 1 becomes the next digit in our result. 
Result so far: 1688.01
Subtracting 77 from 100 leaves us with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Moving on to step 9:
77 goes into 230 2 times with a remainder of 76.
Put 2 as the next digit of the answer. 
Result so far: 1688.012
Subtracting 154 from 230 leaves us with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Step 10:
77 goes into 760 9 times with a remainder of 67.
Record the quotient 9 as the next digit in the result. 
Result so far: 1688.0129
Subtracting 693 from 760 leaves us with 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 11:
When dividing 670 by 77, we get 8 with a remainder of 54.
Put 8 as the next digit of the answer. 
Result so far: 1688.01298
Subtract 616 from 670 to get 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Moving on to step 12:
77 can be fit into 540 7 times, resulting in a remainder of 1.
Record the quotient 7 as the next digit in the result. 
Result so far: 1688.012987
Deduct 539 from 540 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 13:
When dividing 10 by 77, we get 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 1688.012987
If we take 0 away from 10, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 14:
The number 77 fits into 100 1 times, leaving a remainder of 23.
The next digit of our result is 1. 
Result so far: 1688.01298701
The remainder is 23 after subtracting 77 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

The final result is 1688.01298701 with a remainder of 2.3e-08.