We look at the division of 127609 by 25 
Let's see how many times 25 fits into 127609.

On to step 1:
25 can be fit into 1 0 times, resulting in a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (2) from the dividend to 1 and continue with: 12 / 25

Let's proceed to step 2:
If we divide 12 by 25, we get 0 and a remainder of 12.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 12 and we're left with 12.
Grab the next digit (7) from the dividend, add it to 12, then carry on: 127 / 25

Step 3:
127 divided by 25 is 5 with a remainder of 2.
The next digit of our result is 5. 
Result so far: 5.0
If we take 125 away from 127, we end up with 2.
Grab the next digit (6) from the dividend, add it to 2, then carry on: 26 / 25

Moving on to step 4:
If we divide 26 by 25, we get 1 and a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 51.0
If we subtract 25 from 26, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 25

Let's proceed to step 5:
25 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 510.0
If we take 0 away from 10, we end up with 10.
Include the next digit (9) from the dividend after 10, then repeat: 109 / 25

Going ahead to step 6:
109 divided by 25 is 4 with a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 5104.0
Subtract 100 from 109 to get 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Step 7:
The number 25 fits into 90 3 times, leaving a remainder of 15.
Write down 3 as next digit of the result. 
Result so far: 5104.3
Subtracting 75 from 90 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 8:
25 goes into 150 6 times with a remainder of 0.
Put 6 as the next digit of the answer. 
Result so far: 5104.36
Subtracting 150 from 150 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 9:
The number 25 fits into 0 0 times, leaving a remainder of 0.
Put 0 as the next digit of the answer. 
Result so far: 5104.36
Subtract 0 from 0 to get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Advancing to step 10:
If we divide 0 by 25, we get 0 and a remainder of 0.
Use 0 as the next digit of our solution. 
Result so far: 5104.36
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 5104.36 with a balance of 0.0.