103319 ÷ 45 
We're looking to find how many times 45 goes into 103319.

Going ahead to step 1:
When dividing 1 by 45, we get 0 with a remainder of 1.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 45

On to step 2:
The number 45 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Include the next digit (3) from the dividend after 10, then repeat: 103 / 45

Going ahead to step 3:
45 can be fit into 103 2 times, resulting in a remainder of 13.
The next digit of our result is 2. 
Result so far: 2.0
If we subtract 90 from 103, we get 13.
Take the next digit (3) from the dividend and append it to 13, then repeat: 133 / 45

Let's proceed to step 4:
133 divided by 45 is 2 with a remainder of 43.
The next digit of our result is 2. 
Result so far: 22.0
The remainder is 43 after subtracting 90 from 133.
Include the next digit (1) from the dividend after 43, then repeat: 431 / 45

Step 5:
45 can be fit into 431 9 times, resulting in a remainder of 26.
Record the quotient 9 as the next digit in the result. 
Result so far: 229.0
If we take 405 away from 431, we end up with 26.
Fetch the next digit (9) from the dividend, attach it to 26 and continue: 269 / 45

Let's proceed to step 6:
45 can be fit into 269 5 times, resulting in a remainder of 44.
The next digit of our result is 5. 
Result so far: 2295.0
Deduct 225 from 269 and we're left with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 7:
The number 45 fits into 440 9 times, leaving a remainder of 35.
Record the quotient 9 as the next digit in the result. 
Result so far: 2295.9
Subtract 405 from 440 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

On to step 8:
When dividing 350 by 45, we get 7 with a remainder of 35.
Record the quotient 7 as the next digit in the result. 
Result so far: 2295.97
The remainder is 35 after subtracting 315 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 9:
45 can be fit into 350 7 times, resulting in a remainder of 35.
Use 7 as the next digit of our solution. 
Result so far: 2295.977
If we take 315 away from 350, we end up with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

In conclusion, the division gives 2295.977 with a balance of 0.0035.