360003 ÷ 78 
Our goal is to divide 360003 by 78.

Moving on to step 1:
When dividing 3 by 78, we get 0 with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (6) from the dividend, add it to 3, then carry on: 36 / 78

Step 2:
When dividing 36 by 78, we get 0 with a remainder of 36.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 36 to get 36.
Take the next digit (0) from the dividend and append it to 36, then repeat: 360 / 78

Step 3:
360 divided by 78 is 4 with a remainder of 48.
The number 4 becomes the next digit in our result. 
Result so far: 4.0
Deduct 312 from 360 and we're left with 48.
Grab the next digit (0) from the dividend, add it to 48, then carry on: 480 / 78

Going ahead to step 4:
78 can be fit into 480 6 times, resulting in a remainder of 12.
Put 6 as the next digit of the answer. 
Result so far: 46.0
If we take 468 away from 480, we end up with 12.
Bring next digit (0) of the dividend behind the 12 and repeat the process: 120 / 78

On to step 5:
120 divided by 78 is 1 with a remainder of 42.
Write down 1 as next digit of the result. 
Result so far: 461.0
Subtracting 78 from 120 leaves us with 42.
Grab the next digit (3) from the dividend, add it to 42, then carry on: 423 / 78

Going ahead to step 6:
If we divide 423 by 78, we get 5 and a remainder of 33.
The next digit of our result is 5. 
Result so far: 4615.0
If we subtract 390 from 423, we get 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Going ahead to step 7:
When dividing 330 by 78, we get 4 with a remainder of 18.
The number 4 becomes the next digit in our result. 
Result so far: 4615.4
Deduct 312 from 330 and we're left with 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

On to step 8:
78 goes into 180 2 times with a remainder of 24.
The number 2 becomes the next digit in our result. 
Result so far: 4615.42
If we subtract 156 from 180, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 9:
When dividing 240 by 78, we get 3 with a remainder of 6.
The next digit of our result is 3. 
Result so far: 4615.423
The remainder is 6 after subtracting 234 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 60, and continue the process.

Advancing to step 10:
When dividing 60 by 78, we get 0 with a remainder of 60.
Record the quotient 0 as the next digit in the result. 
Result so far: 4615.423
If we take 0 away from 60, we end up with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 11:
78 goes into 600 7 times with a remainder of 54.
Put 7 as the next digit of the answer. 
Result so far: 4615.42307
If we take 546 away from 600, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

On to step 12:
The number 78 fits into 540 6 times, leaving a remainder of 72.
Use 6 as the next digit of our solution. 
Result so far: 4615.423076
The remainder is 72 after subtracting 468 from 540.
Since there are no more digits in the dividend, we add a zero to the remainder making it 720, and continue the process.

Let's proceed to step 13:
The number 78 fits into 720 9 times, leaving a remainder of 18.
The number 9 becomes the next digit in our result. 
Result so far: 4615.4230769
Subtract 702 from 720 to get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

Step 14:
If we divide 180 by 78, we get 2 and a remainder of 24.
Use 2 as the next digit of our solution. 
Result so far: 4615.42307692
The remainder is 24 after subtracting 156 from 180.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

After the division, we end up with 4615.42307692 and a remainder of 2.4e-08.