We're dividing 145200 by 45 
We're looking to find how many times 45 goes into 145200.

Going ahead to step 1:
If we divide 1 by 45, we get 0 and a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Take the next digit (4) from the dividend and append it to 1, then repeat: 14 / 45

On to step 2:
When dividing 14 by 45, we get 0 with a remainder of 14.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 14, we get 14.
Grab the next digit (5) from the dividend, add it to 14, then carry on: 145 / 45

Step 3:
45 can be fit into 145 3 times, resulting in a remainder of 10.
Use 3 as the next digit of our solution. 
Result so far: 3.0
The remainder is 10 after subtracting 135 from 145.
Bring next digit (2) of the dividend behind the 10 and repeat the process: 102 / 45

Advancing to step 4:
The number 45 fits into 102 2 times, leaving a remainder of 12.
Write down 2 as next digit of the result. 
Result so far: 32.0
Subtract 90 from 102 to get 12.
Append the next digit (0) from the dividend to 12 and continue with: 120 / 45

On to step 5:
The number 45 fits into 120 2 times, leaving a remainder of 30.
Use 2 as the next digit of our solution. 
Result so far: 322.0
Subtract 90 from 120 to get 30.
Fetch the next digit (0) from the dividend, attach it to 30 and continue: 300 / 45

Let's proceed to step 6:
45 goes into 300 6 times with a remainder of 30.
Record the quotient 6 as the next digit in the result. 
Result so far: 3226.0
Subtracting 270 from 300 leaves us with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 7:
45 can be fit into 300 6 times, resulting in a remainder of 30.
The next digit of our result is 6. 
Result so far: 3226.6
Subtract 270 from 300 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 8:
300 divided by 45 is 6 with a remainder of 30.
Put 6 as the next digit of the answer. 
Result so far: 3226.66
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

In conclusion, the division gives 3226.66 with a balance of 0.03.