5181 ÷ 78 
We want to divide 5181 by 78.

Step 1:
The number 78 fits into 5 0 times, leaving a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 5 leaves us with 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 78

Moving on to step 2:
The number 78 fits into 51 0 times, leaving a remainder of 51.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 51, we get 51.
Take the next digit (8) from the dividend and append it to 51, then repeat: 518 / 78

Moving on to step 3:
78 can be fit into 518 6 times, resulting in a remainder of 50.
Use 6 as the next digit of our solution. 
Result so far: 6.0
Subtract 468 from 518 to get 50.
Grab the next digit (1) from the dividend, add it to 50, then carry on: 501 / 78

On to step 4:
501 divided by 78 is 6 with a remainder of 33.
Put 6 as the next digit of the answer. 
Result so far: 66.0
If we take 468 away from 501, we end up with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Step 5:
The number 78 fits into 330 4 times, leaving a remainder of 18.
The number 4 becomes the next digit in our result. 
Result so far: 66.4
If we subtract 312 from 330, we 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.

Let's proceed to step 6:
180 divided by 78 is 2 with a remainder of 24.
Write down 2 as next digit of the result. 
Result so far: 66.42
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.

On to step 7:
240 divided by 78 is 3 with a remainder of 6.
Write down 3 as next digit of the result. 
Result so far: 66.423
If we subtract 234 from 240, 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.

Going ahead to step 8:
78 can be fit into 60 0 times, resulting in a remainder of 60.
The number 0 becomes the next digit in our result. 
Result so far: 66.423
Subtracting 0 from 60 leaves us 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.

Moving on to step 9:
When dividing 600 by 78, we get 7 with a remainder of 54.
The number 7 becomes the next digit in our result. 
Result so far: 66.42307
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 10:
540 divided by 78 is 6 with a remainder of 72.
Write down 6 as next digit of the result. 
Result so far: 66.423076
Subtracting 468 from 540 leaves us with 72.
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 11:
720 divided by 78 is 9 with a remainder of 18.
The number 9 becomes the next digit in our result. 
Result so far: 66.4230769
If we take 702 away from 720, we end up 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.

Going ahead to step 12:
The number 78 fits into 180 2 times, leaving a remainder of 24.
The number 2 becomes the next digit in our result. 
Result so far: 66.42307692
Subtract 156 from 180 to 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.

Our division results in 66.42307692 with a remaining 2.4e-08.