105388 divided by 45 
Our goal is to divide 105388 by 45.

Step 1:
If we divide 1 by 45, we get 0 and a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 1 and we're left with 1.
Take the next digit (0) from the dividend and append it to 1, then repeat: 10 / 45

Advancing to step 2:
When dividing 10 by 45, we get 0 with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 45

On to step 3:
When dividing 105 by 45, we get 2 with a remainder of 15.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtract 90 from 105 to get 15.
Grab the next digit (3) from the dividend, add it to 15, then carry on: 153 / 45

Let's proceed to step 4:
The number 45 fits into 153 3 times, leaving a remainder of 18.
The next digit of our result is 3. 
Result so far: 23.0
If we subtract 135 from 153, we get 18.
Grab the next digit (8) from the dividend, add it to 18, then carry on: 188 / 45

Step 5:
45 goes into 188 4 times with a remainder of 8.
The next digit of our result is 4. 
Result so far: 234.0
If we subtract 180 from 188, we get 8.
Append the next digit (8) from the dividend to 8 and continue with: 88 / 45

Let's proceed to step 6:
The number 45 fits into 88 1 times, leaving a remainder of 43.
Use 1 as the next digit of our solution. 
Result so far: 2341.0
If we take 45 away from 88, we end up with 43.
Since there are no more digits in the dividend, we add a zero to the remainder making it 430, and continue the process.

Moving on to step 7:
When dividing 430 by 45, we get 9 with a remainder of 25.
Put 9 as the next digit of the answer. 
Result so far: 2341.9
Subtracting 405 from 430 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 8:
When dividing 250 by 45, we get 5 with a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 2341.95
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 9:
250 divided by 45 is 5 with a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 2341.955
The remainder is 25 after subtracting 225 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

In conclusion, the division gives 2341.955 with a balance of 0.0025.