We look at the division of 107825 by 89 
We want to figure out the number of times 107825 can be divided by 89.

Advancing to step 1:
1 divided by 89 is 0 with a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 89

On to step 2:
When dividing 10 by 89, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Append the next digit (7) from the dividend to 10 and continue with: 107 / 89

Moving on to step 3:
89 can be fit into 107 1 times, resulting in a remainder of 18.
The next digit of our result is 1. 
Result so far: 1.0
Deduct 89 from 107 and we're left with 18.
Include the next digit (8) from the dividend after 18, then repeat: 188 / 89

Going ahead to step 4:
188 divided by 89 is 2 with a remainder of 10.
Record the quotient 2 as the next digit in the result. 
Result so far: 12.0
The remainder is 10 after subtracting 178 from 188.
Take the next digit (2) from the dividend and append it to 10, then repeat: 102 / 89

On to step 5:
102 divided by 89 is 1 with a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 121.0
If we take 89 away from 102, we end up with 13.
Append the next digit (5) from the dividend to 13 and continue with: 135 / 89

Moving on to step 6:
135 divided by 89 is 1 with a remainder of 46.
Use 1 as the next digit of our solution. 
Result so far: 1211.0
Deduct 89 from 135 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 7:
89 can be fit into 460 5 times, resulting in a remainder of 15.
Record the quotient 5 as the next digit in the result. 
Result so far: 1211.5
If we subtract 445 from 460, we get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 8:
89 can be fit into 150 1 times, resulting in a remainder of 61.
Write down 1 as next digit of the result. 
Result so far: 1211.51
If we take 89 away from 150, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Let's proceed to step 9:
When dividing 610 by 89, we get 6 with a remainder of 76.
The number 6 becomes the next digit in our result. 
Result so far: 1211.516
If we take 534 away from 610, we end up 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.

Advancing to step 10:
If we divide 760 by 89, we get 8 and a remainder of 48.
Record the quotient 8 as the next digit in the result. 
Result so far: 1211.5168
If we take 712 away from 760, we end up with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Let's proceed to step 11:
89 goes into 480 5 times with a remainder of 35.
The number 5 becomes the next digit in our result. 
Result so far: 1211.51685
If we take 445 away from 480, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 12:
89 goes into 350 3 times with a remainder of 83.
Write down 3 as next digit of the result. 
Result so far: 1211.516853
If we take 267 away from 350, we end up with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Advancing to step 13:
If we divide 830 by 89, we get 9 and a remainder of 29.
The number 9 becomes the next digit in our result. 
Result so far: 1211.5168539
Subtract 801 from 830 to get 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 14:
89 goes into 290 3 times with a remainder of 23.
The number 3 becomes the next digit in our result. 
Result so far: 1211.51685393
Subtracting 267 from 290 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.

In conclusion, the division gives 1211.51685393 with a balance of 2.3e-08.