We're dividing 824521 by 78 
Our goal is to divide 824521 by 78.

Going ahead to step 1:
If we divide 8 by 78, we get 0 and a remainder of 8.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 8 to get 8.
Take the next digit (2) from the dividend and append it to 8, then repeat: 82 / 78

Advancing to step 2:
78 can be fit into 82 1 times, resulting in a remainder of 4.
Write down 1 as next digit of the result. 
Result so far: 1.0
Subtract 78 from 82 to get 4.
Include the next digit (4) from the dividend after 4, then repeat: 44 / 78

Moving on to step 3:
If we divide 44 by 78, we get 0 and a remainder of 44.
Use 0 as the next digit of our solution. 
Result so far: 10.0
Subtract 0 from 44 to get 44.
Take the next digit (5) from the dividend and append it to 44, then repeat: 445 / 78

Advancing to step 4:
78 can be fit into 445 5 times, resulting in a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 105.0
Subtract 390 from 445 to get 55.
Take the next digit (2) from the dividend and append it to 55, then repeat: 552 / 78

Let's proceed to step 5:
When dividing 552 by 78, we get 7 with a remainder of 6.
The number 7 becomes the next digit in our result. 
Result so far: 1057.0
Subtract 546 from 552 to get 6.
Fetch the next digit (1) from the dividend, attach it to 6 and continue: 61 / 78

Advancing to step 6:
When dividing 61 by 78, we get 0 with a remainder of 61.
Write down 0 as next digit of the result. 
Result so far: 10570.0
If we subtract 0 from 61, we get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 7:
610 divided by 78 is 7 with a remainder of 64.
The next digit of our result is 7. 
Result so far: 10570.7
The remainder is 64 after subtracting 546 from 610.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

On to step 8:
78 goes into 640 8 times with a remainder of 16.
The next digit of our result is 8. 
Result so far: 10570.78
Deduct 624 from 640 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 9:
If we divide 160 by 78, we get 2 and a remainder of 4.
Record the quotient 2 as the next digit in the result. 
Result so far: 10570.782
Deduct 156 from 160 and we're left 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.

Let's proceed to step 10:
78 can be fit into 40 0 times, resulting in a remainder of 40.
Write down 0 as next digit of the result. 
Result so far: 10570.782
If we take 0 away from 40, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 11:
400 divided by 78 is 5 with a remainder of 10.
Record the quotient 5 as the next digit in the result. 
Result so far: 10570.78205
Deduct 390 from 400 and we're left 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.

Going ahead to step 12:
78 goes into 100 1 times with a remainder of 22.
Write down 1 as next digit of the result. 
Result so far: 10570.782051
Subtracting 78 from 100 leaves us with 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

On to step 13:
78 goes into 220 2 times with a remainder of 64.
The number 2 becomes the next digit in our result. 
Result so far: 10570.7820512
Subtract 156 from 220 to get 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Going ahead to step 14:
78 goes into 640 8 times with a remainder of 16.
Write down 8 as next digit of the result. 
Result so far: 10570.78205128
Deduct 624 from 640 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

In conclusion, the division gives 10570.78205128 with a balance of 1.6e-08.