We look at the division of 375825 by 9 
Our goal is to divide 375825 by 9.

Advancing to step 1:
3 divided by 9 is 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (7) from the dividend to 3 and continue with: 37 / 9

Moving on to step 2:
9 can be fit into 37 4 times, resulting in a remainder of 1.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
If we subtract 36 from 37, we get 1.
Fetch the next digit (5) from the dividend, attach it to 1 and continue: 15 / 9

Going ahead to step 3:
The number 9 fits into 15 1 times, leaving a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 41.0
If we take 9 away from 15, we end up with 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 9

On to step 4:
9 goes into 68 7 times with a remainder of 5.
The next digit of our result is 7. 
Result so far: 417.0
Subtract 63 from 68 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 9

On to step 5:
If we divide 52 by 9, we get 5 and a remainder of 7.
Put 5 as the next digit of the answer. 
Result so far: 4175.0
If we subtract 45 from 52, we get 7.
Grab the next digit (5) from the dividend, add it to 7, then carry on: 75 / 9

Let's proceed to step 6:
When dividing 75 by 9, we get 8 with a remainder of 3.
Put 8 as the next digit of the answer. 
Result so far: 41758.0
If we take 72 away from 75, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 7:
30 divided by 9 is 3 with a remainder of 3.
The number 3 becomes the next digit in our result. 
Result so far: 41758.3
If we take 27 away from 30, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Let's proceed to step 8:
30 divided by 9 is 3 with a remainder of 3.
The next digit of our result is 3. 
Result so far: 41758.33
Subtracting 27 from 30 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

The final result is 41758.33 with a remainder of 0.003.