Let's divide 379001 by 19
Our goal is to divide 379001 by 19.

On to step 1:
If we divide 3 by 19, we get 0 and a remainder of 3.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (7) from the dividend, attach it to 3 and continue: 37 / 19

Going ahead to step 2:
19 can be fit into 37 1 times, resulting in a remainder of 18.
Put 1 as the next digit of the answer. 
Result so far: 1.0
The remainder is 18 after subtracting 19 from 37.
Take the next digit (9) from the dividend and append it to 18, then repeat: 189 / 19

Moving on to step 3:
When dividing 189 by 19, we get 9 with a remainder of 18.
Put 9 as the next digit of the answer. 
Result so far: 19.0
Subtracting 171 from 189 leaves us with 18.
Take the next digit (0) from the dividend and append it to 18, then repeat: 180 / 19

Step 4:
The number 19 fits into 180 9 times, leaving a remainder of 9.
Record the quotient 9 as the next digit in the result. 
Result so far: 199.0
The remainder is 9 after subtracting 171 from 180.
Fetch the next digit (0) from the dividend, attach it to 9 and continue: 90 / 19

Going ahead to step 5:
90 divided by 19 is 4 with a remainder of 14.
Use 4 as the next digit of our solution. 
Result so far: 1994.0
Subtract 76 from 90 to get 14.
Fetch the next digit (1) from the dividend, attach it to 14 and continue: 141 / 19

Going ahead to step 6:
When dividing 141 by 19, we get 7 with a remainder of 8.
The number 7 becomes the next digit in our result. 
Result so far: 19947.0
The remainder is 8 after subtracting 133 from 141.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 7:
If we divide 80 by 19, we get 4 and a remainder of 4.
Use 4 as the next digit of our solution. 
Result so far: 19947.4
Subtracting 76 from 80 leaves us with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Advancing to step 8:
19 goes into 40 2 times with a remainder of 2.
The number 2 becomes the next digit in our result. 
Result so far: 19947.42
Subtract 38 from 40 to get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

On to step 9:
19 goes into 20 1 times with a remainder of 1.
Use 1 as the next digit of our solution. 
Result so far: 19947.421
If we take 19 away from 20, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 10:
When dividing 10 by 19, we get 0 with a remainder of 10.
The next digit of our result is 0. 
Result so far: 19947.421
The remainder is 10 after subtracting 0 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 11:
19 goes into 100 5 times with a remainder of 5.
Write down 5 as next digit of the result. 
Result so far: 19947.42105
If we subtract 95 from 100, we 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 12:
The number 19 fits into 50 2 times, leaving a remainder of 12.
Put 2 as the next digit of the answer. 
Result so far: 19947.421052
If we take 38 away from 50, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

Let's proceed to step 13:
When dividing 120 by 19, we get 6 with a remainder of 6.
Record the quotient 6 as the next digit in the result. 
Result so far: 19947.4210526
The remainder is 6 after subtracting 114 from 120.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Going ahead to step 14:
The number 19 fits into 60 3 times, leaving a remainder of 3.
Put 3 as the next digit of the answer. 
Result so far: 19947.42105263
Deduct 57 from 60 and we're left 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.

After the division, we end up with 19947.42105263 and a remainder of 3e-09.