We're dividing 105569 by 48 
We're looking to find how many times 48 goes into 105569.

Advancing to step 1:
If we divide 1 by 48, we get 0 and a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Include the next digit (0) from the dividend after 1, then repeat: 10 / 48

Going ahead to step 2:
10 divided by 48 is 0 with a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 10 after subtracting 0 from 10.
Append the next digit (5) from the dividend to 10 and continue with: 105 / 48

Let's proceed to step 3:
The number 48 fits into 105 2 times, leaving a remainder of 9.
Write down 2 as next digit of the result. 
Result so far: 2.0
Subtracting 96 from 105 leaves us with 9.
Append the next digit (5) from the dividend to 9 and continue with: 95 / 48

Step 4:
48 goes into 95 1 times with a remainder of 47.
Write down 1 as next digit of the result. 
Result so far: 21.0
The remainder is 47 after subtracting 48 from 95.
Bring next digit (6) of the dividend behind the 47 and repeat the process: 476 / 48

Advancing to step 5:
The number 48 fits into 476 9 times, leaving a remainder of 44.
Write down 9 as next digit of the result. 
Result so far: 219.0
Deduct 432 from 476 and we're left with 44.
Fetch the next digit (9) from the dividend, attach it to 44 and continue: 449 / 48

Going ahead to step 6:
449 divided by 48 is 9 with a remainder of 17.
The number 9 becomes the next digit in our result. 
Result so far: 2199.0
Subtract 432 from 449 to get 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Advancing to step 7:
If we divide 170 by 48, we get 3 and a remainder of 26.
Use 3 as the next digit of our solution. 
Result so far: 2199.3
The remainder is 26 after subtracting 144 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

Moving on to step 8:
When dividing 260 by 48, we get 5 with a remainder of 20.
Record the quotient 5 as the next digit in the result. 
Result so far: 2199.35
Subtracting 240 from 260 leaves us with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

On to step 9:
If we divide 200 by 48, we get 4 and a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 2199.354
Subtracting 192 from 200 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 10:
The number 48 fits into 80 1 times, leaving a remainder of 32.
Put 1 as the next digit of the answer. 
Result so far: 2199.3541
If we subtract 48 from 80, we get 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Moving on to step 11:
320 divided by 48 is 6 with a remainder of 32.
Record the quotient 6 as the next digit in the result. 
Result so far: 2199.35416
If we take 288 away from 320, we end up with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Advancing to step 12:
If we divide 320 by 48, we get 6 and a remainder of 32.
Use 6 as the next digit of our solution. 
Result so far: 2199.354166
The remainder is 32 after subtracting 288 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

In conclusion, the division gives 2199.354166 with a balance of 3.2e-06.