We look at the division of 378552 by 9 
We're looking to find how many times 9 goes into 378552.

Moving on to step 1:
9 goes into 3 0 times with a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 9

Moving on to step 2:
37 divided by 9 is 4 with a remainder of 1.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 36 from 37 and we're left with 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 9

Moving on to step 3:
The number 9 fits into 18 2 times, leaving a remainder of 0.
Put 2 as the next digit of the answer. 
Result so far: 42.0
If we take 18 away from 18, we end up with 0.
Bring next digit (5) of the dividend behind the 0 and repeat the process: 5 / 9

Step 4:
9 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 420.0
Subtract 0 from 5 to get 5.
Bring next digit (5) of the dividend behind the 5 and repeat the process: 55 / 9

Going ahead to step 5:
55 divided by 9 is 6 with a remainder of 1.
Record the quotient 6 as the next digit in the result. 
Result so far: 4206.0
Subtract 54 from 55 to get 1.
Take the next digit (2) from the dividend and append it to 1, then repeat: 12 / 9

Going ahead to step 6:
When dividing 12 by 9, we get 1 with a remainder of 3.
Put 1 as the next digit of the answer. 
Result so far: 42061.0
Subtract 9 from 12 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 7:
9 can be fit into 30 3 times, resulting in a remainder of 3.
Record the quotient 3 as the next digit in the result. 
Result so far: 42061.3
Subtract 27 from 30 to get 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Advancing to step 8:
When dividing 30 by 9, we get 3 with a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 42061.33
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.

After the division, we end up with 42061.33 and a remainder of 0.003.