133825 ÷ 15 
Our goal is to divide 133825 by 15.

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
If we take 0 away from 1, we end up with 1.
Grab the next digit (3) from the dividend, add it to 1, then carry on: 13 / 15

Moving on to step 2:
15 goes into 13 0 times with a remainder of 13.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 13, we get 13.
Include the next digit (3) from the dividend after 13, then repeat: 133 / 15

Advancing to step 3:
133 divided by 15 is 8 with a remainder of 13.
The number 8 becomes the next digit in our result. 
Result so far: 8.0
The remainder is 13 after subtracting 120 from 133.
Take the next digit (8) from the dividend and append it to 13, then repeat: 138 / 15

Going ahead to step 4:
When dividing 138 by 15, we get 9 with a remainder of 3.
The number 9 becomes the next digit in our result. 
Result so far: 89.0
Deduct 135 from 138 and we're left with 3.
Fetch the next digit (2) from the dividend, attach it to 3 and continue: 32 / 15

Moving on to step 5:
15 goes into 32 2 times with a remainder of 2.
Put 2 as the next digit of the answer. 
Result so far: 892.0
Subtract 30 from 32 to get 2.
Take the next digit (5) from the dividend and append it to 2, then repeat: 25 / 15

On to step 6:
The number 15 fits into 25 1 times, leaving a remainder of 10.
The next digit of our result is 1. 
Result so far: 8921.0
Subtract 15 from 25 to get 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.
Put 6 as the next digit of the answer. 
Result so far: 8921.6
Deduct 90 from 100 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.

Step 8:
100 divided by 15 is 6 with a remainder of 10.
The number 6 becomes the next digit in our result. 
Result so far: 8921.66
Deduct 90 from 100 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.

In conclusion, the division gives 8921.66 with a balance of 0.01.