We look at the division of 338468 by 45 
Let's see how many times 45 fits into 338468.

Going ahead to step 1:
3 divided by 45 is 0 with a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 45

Advancing to step 2:
When dividing 33 by 45, we get 0 with a remainder of 33.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 33, we end up with 33.
Take the next digit (8) from the dividend and append it to 33, then repeat: 338 / 45

Going ahead to step 3:
The number 45 fits into 338 7 times, leaving a remainder of 23.
Put 7 as the next digit of the answer. 
Result so far: 7.0
If we subtract 315 from 338, we get 23.
Include the next digit (4) from the dividend after 23, then repeat: 234 / 45

Going ahead to step 4:
If we divide 234 by 45, we get 5 and a remainder of 9.
Record the quotient 5 as the next digit in the result. 
Result so far: 75.0
If we take 225 away from 234, we end up with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 45

On to step 5:
45 can be fit into 96 2 times, resulting in a remainder of 6.
The number 2 becomes the next digit in our result. 
Result so far: 752.0
Subtract 90 from 96 to get 6.
Fetch the next digit (8) from the dividend, attach it to 6 and continue: 68 / 45

Advancing to step 6:
If we divide 68 by 45, we get 1 and a remainder of 23.
Put 1 as the next digit of the answer. 
Result so far: 7521.0
Deduct 45 from 68 and we're left with 23.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Advancing to step 7:
45 goes into 230 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 7521.5
If we take 225 away from 230, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Moving on to step 8:
If we divide 50 by 45, we get 1 and a remainder of 5.
Use 1 as the next digit of our solution. 
Result so far: 7521.51
If we take 45 away from 50, we end up with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 9:
45 can be fit into 50 1 times, resulting in a remainder of 5.
Write down 1 as next digit of the result. 
Result so far: 7521.511
Subtracting 45 from 50 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

The final result is 7521.511 with a remainder of 0.0005.