105 ÷ 19 
Let's see how many times 19 fits into 105.

Let's proceed to step 1:
The number 19 fits into 1 0 times, leaving a remainder of 1.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Append the next digit (0) from the dividend to 1 and continue with: 10 / 19

Moving on to step 2:
19 goes into 10 0 times with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 10 to get 10.
Take the next digit (5) from the dividend and append it to 10, then repeat: 105 / 19

Advancing to step 3:
19 can be fit into 105 5 times, resulting in a remainder of 10.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we take 95 away from 105, we end up with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 4:
100 divided by 19 is 5 with a remainder of 5.
Put 5 as the next digit of the answer. 
Result so far: 5.5
Subtract 95 from 100 to get 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 5:
When dividing 50 by 19, we get 2 with a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 5.52
The remainder is 12 after subtracting 38 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Going ahead to step 6:
19 can be fit into 120 6 times, resulting in a remainder of 6.
Write down 6 as next digit of the result. 
Result so far: 5.526
If we subtract 114 from 120, we get 6.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Step 7:
If we divide 60 by 19, we get 3 and a remainder of 3.
Write down 3 as next digit of the result. 
Result so far: 5.5263
If we take 57 away from 60, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Going ahead to step 8:
19 goes into 30 1 times with a remainder of 11.
Put 1 as the next digit of the answer. 
Result so far: 5.52631
If we subtract 19 from 30, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Advancing to step 9:
When dividing 110 by 19, we get 5 with a remainder of 15.
Use 5 as the next digit of our solution. 
Result so far: 5.526315
If we take 95 away from 110, we end up with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 10:
19 goes into 150 7 times with a remainder of 17.
The next digit of our result is 7. 
Result so far: 5.5263157
Deduct 133 from 150 and we're left with 17.
Since there are no more digits in the dividend, we add a zero to the remainder making it 170, and continue the process.

Step 11:
19 can be fit into 170 8 times, resulting in a remainder of 18.
Use 8 as the next digit of our solution. 
Result so far: 5.52631578
The remainder is 18 after subtracting 152 from 170.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 5.52631578 and a remainder of 1.8e-08.