We look at the division of 689906 by 78 
The aim is to understand the frequency of 78 in 689906.

Step 1:
6 divided by 78 is 0 with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Take the next digit (8) from the dividend and append it to 6, then repeat: 68 / 78

Going ahead to step 2:
When dividing 68 by 78, we get 0 with a remainder of 68.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 68 after subtracting 0 from 68.
Bring next digit (9) of the dividend behind the 68 and repeat the process: 689 / 78

Moving on to step 3:
78 goes into 689 8 times with a remainder of 65.
Put 8 as the next digit of the answer. 
Result so far: 8.0
Deduct 624 from 689 and we're left with 65.
Fetch the next digit (9) from the dividend, attach it to 65 and continue: 659 / 78

On to step 4:
78 goes into 659 8 times with a remainder of 35.
The next digit of our result is 8. 
Result so far: 88.0
Subtract 624 from 659 to get 35.
Bring next digit (0) of the dividend behind the 35 and repeat the process: 350 / 78

Going ahead to step 5:
78 goes into 350 4 times with a remainder of 38.
Use 4 as the next digit of our solution. 
Result so far: 884.0
The remainder is 38 after subtracting 312 from 350.
Bring next digit (6) of the dividend behind the 38 and repeat the process: 386 / 78

On to step 6:
When dividing 386 by 78, we get 4 with a remainder of 74.
Record the quotient 4 as the next digit in the result. 
Result so far: 8844.0
If we take 312 away from 386, we end up with 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Let's proceed to step 7:
When dividing 740 by 78, we get 9 with a remainder of 38.
The next digit of our result is 9. 
Result so far: 8844.9
Subtracting 702 from 740 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Let's proceed to step 8:
When dividing 380 by 78, we get 4 with a remainder of 68.
Use 4 as the next digit of our solution. 
Result so far: 8844.94
Subtract 312 from 380 to get 68.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

Let's proceed to step 9:
680 divided by 78 is 8 with a remainder of 56.
Use 8 as the next digit of our solution. 
Result so far: 8844.948
The remainder is 56 after subtracting 624 from 680.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Step 10:
When dividing 560 by 78, we get 7 with a remainder of 14.
The next digit of our result is 7. 
Result so far: 8844.9487
If we take 546 away from 560, we end up 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.

Going ahead to step 11:
140 divided by 78 is 1 with a remainder of 62.
Record the quotient 1 as the next digit in the result. 
Result so far: 8844.94871
The remainder is 62 after subtracting 78 from 140.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 12:
78 goes into 620 7 times with a remainder of 74.
Use 7 as the next digit of our solution. 
Result so far: 8844.948717
If we subtract 546 from 620, we get 74.
Since there are no more digits in the dividend, we add a zero to the remainder making it 740, and continue the process.

Going ahead to step 13:
78 can be fit into 740 9 times, resulting in a remainder of 38.
Put 9 as the next digit of the answer. 
Result so far: 8844.9487179
If we take 702 away from 740, we end up with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

Advancing to step 14:
When dividing 380 by 78, we get 4 with a remainder of 68.
Record the quotient 4 as the next digit in the result. 
Result so far: 8844.94871794
The remainder is 68 after subtracting 312 from 380.
Since there are no more digits in the dividend, we add a zero to the remainder making it 680, and continue the process.

After the division, we end up with 8844.94871794 and a remainder of 6.8e-08.