We're dividing 101725 by 15 
Our goal is to divide 101725 by 15.

Advancing to step 1:
When dividing 1 by 15, we get 0 with a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 15

Moving on to step 2:
15 goes into 10 0 times with a remainder of 10.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Append the next digit (1) from the dividend to 10 and continue with: 101 / 15

On to step 3:
When dividing 101 by 15, we get 6 with a remainder of 11.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we take 90 away from 101, we end up with 11.
Take the next digit (7) from the dividend and append it to 11, then repeat: 117 / 15

On to step 4:
15 can be fit into 117 7 times, resulting in a remainder of 12.
Write down 7 as next digit of the result. 
Result so far: 67.0
Deduct 105 from 117 and we're left with 12.
Grab the next digit (2) from the dividend, add it to 12, then carry on: 122 / 15

Going ahead to step 5:
122 divided by 15 is 8 with a remainder of 2.
Put 8 as the next digit of the answer. 
Result so far: 678.0
If we take 120 away from 122, we end up with 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 15

Going ahead to step 6:
If we divide 25 by 15, we get 1 and a remainder of 10.
Use 1 as the next digit of our solution. 
Result so far: 6781.0
If we take 15 away from 25, 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.

Moving on to step 7:
100 divided by 15 is 6 with a remainder of 10.
The next digit of our result is 6. 
Result so far: 6781.6
Subtracting 90 from 100 leaves us 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 8:
When dividing 100 by 15, we get 6 with a remainder of 10.
Use 6 as the next digit of our solution. 
Result so far: 6781.66
The remainder is 10 after subtracting 90 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

In conclusion, the division gives 6781.66 with a balance of 0.01.