We look at the division of 821101 by 78 
We're looking to find how many times 78 goes into 821101.

On to step 1:
78 goes into 8 0 times with a remainder of 8.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 78

On to step 2:
82 divided by 78 is 1 with a remainder of 4.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
The remainder is 4 after subtracting 78 from 82.
Bring next digit (1) of the dividend behind the 4 and repeat the process: 41 / 78

Let's proceed to step 3:
If we divide 41 by 78, we get 0 and a remainder of 41.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
The remainder is 41 after subtracting 0 from 41.
Bring next digit (1) of the dividend behind the 41 and repeat the process: 411 / 78

Let's proceed to step 4:
The number 78 fits into 411 5 times, leaving a remainder of 21.
Record the quotient 5 as the next digit in the result. 
Result so far: 105.0
Subtracting 390 from 411 leaves us with 21.
Fetch the next digit (0) from the dividend, attach it to 21 and continue: 210 / 78

Going ahead to step 5:
If we divide 210 by 78, we get 2 and a remainder of 54.
The number 2 becomes the next digit in our result. 
Result so far: 1052.0
Subtract 156 from 210 to get 54.
Fetch the next digit (1) from the dividend, attach it to 54 and continue: 541 / 78

Going ahead to step 6:
541 divided by 78 is 6 with a remainder of 73.
Write down 6 as next digit of the result. 
Result so far: 10526.0
Subtract 468 from 541 to get 73.
Since there are no more digits in the dividend, we add a zero to the remainder making it 730, and continue the process.

Moving on to step 7:
730 divided by 78 is 9 with a remainder of 28.
Put 9 as the next digit of the answer. 
Result so far: 10526.9
If we take 702 away from 730, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Step 8:
The number 78 fits into 280 3 times, leaving a remainder of 46.
Write down 3 as next digit of the result. 
Result so far: 10526.93
Subtracting 234 from 280 leaves us with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 9:
The number 78 fits into 460 5 times, leaving a remainder of 70.
Put 5 as the next digit of the answer. 
Result so far: 10526.935
Deduct 390 from 460 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 10:
78 can be fit into 700 8 times, resulting in a remainder of 76.
The next digit of our result is 8. 
Result so far: 10526.9358
Deduct 624 from 700 and we're left with 76.
Since there are no more digits in the dividend, we add a zero to the remainder making it 760, and continue the process.

Let's proceed to step 11:
When dividing 760 by 78, we get 9 with a remainder of 58.
Use 9 as the next digit of our solution. 
Result so far: 10526.93589
The remainder is 58 after subtracting 702 from 760.
Since there are no more digits in the dividend, we add a zero to the remainder making it 580, and continue the process.

On to step 12:
When dividing 580 by 78, we get 7 with a remainder of 34.
Use 7 as the next digit of our solution. 
Result so far: 10526.935897
Deduct 546 from 580 and we're left with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 13:
340 divided by 78 is 4 with a remainder of 28.
Put 4 as the next digit of the answer. 
Result so far: 10526.9358974
Subtracting 312 from 340 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 14:
280 divided by 78 is 3 with a remainder of 46.
Use 3 as the next digit of our solution. 
Result so far: 10526.93589743
Deduct 234 from 280 and we're left with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

In conclusion, the division gives 10526.93589743 with a balance of 4.6e-08.