516821 divided by 78 
Our goal is to divide 516821 by 78.

On to step 1:
5 divided by 78 is 0 with a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 5, we end up with 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 78

Going ahead to step 2:
When dividing 51 by 78, we get 0 with a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Append the next digit (6) from the dividend to 51 and continue with: 516 / 78

On to step 3:
78 can be fit into 516 6 times, resulting in a remainder of 48.
Write down 6 as next digit of the result. 
Result so far: 6.0
If we subtract 468 from 516, we get 48.
Take the next digit (8) from the dividend and append it to 48, then repeat: 488 / 78

Moving on to step 4:
When dividing 488 by 78, we get 6 with a remainder of 20.
The next digit of our result is 6. 
Result so far: 66.0
If we subtract 468 from 488, we get 20.
Append the next digit (2) from the dividend to 20 and continue with: 202 / 78

On to step 5:
202 divided by 78 is 2 with a remainder of 46.
Put 2 as the next digit of the answer. 
Result so far: 662.0
Subtract 156 from 202 to get 46.
Append the next digit (1) from the dividend to 46 and continue with: 461 / 78

Moving on to step 6:
The number 78 fits into 461 5 times, leaving a remainder of 71.
Put 5 as the next digit of the answer. 
Result so far: 6625.0
Deduct 390 from 461 and we're left with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Going ahead to step 7:
The number 78 fits into 710 9 times, leaving a remainder of 8.
Write down 9 as next digit of the result. 
Result so far: 6625.9
If we take 702 away from 710, we end up 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.

Going ahead to step 8:
80 divided by 78 is 1 with a remainder of 2.
The next digit of our result is 1. 
Result so far: 6625.91
If we subtract 78 from 80, we 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.

Let's proceed to step 9:
If we divide 20 by 78, we get 0 and a remainder of 20.
Write down 0 as next digit of the result. 
Result so far: 6625.91
The remainder is 20 after subtracting 0 from 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 10:
If we divide 200 by 78, we get 2 and a remainder of 44.
Use 2 as the next digit of our solution. 
Result so far: 6625.9102
Subtracting 156 from 200 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 11:
440 divided by 78 is 5 with a remainder of 50.
The next digit of our result is 5. 
Result so far: 6625.91025
The remainder is 50 after subtracting 390 from 440.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Going ahead to step 12:
78 can be fit into 500 6 times, resulting in a remainder of 32.
The next digit of our result is 6. 
Result so far: 6625.910256
Subtracting 468 from 500 leaves us 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.

Going ahead to step 13:
78 goes into 320 4 times with a remainder of 8.
Use 4 as the next digit of our solution. 
Result so far: 6625.9102564
The remainder is 8 after subtracting 312 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Step 14:
78 can be fit into 80 1 times, resulting in a remainder of 2.
The next digit of our result is 1. 
Result so far: 6625.91025641
If we subtract 78 from 80, we 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.

Our division results in 6625.91025641 with a remaining 2e-09.