2877669 ÷ 963 
Our goal is to divide 2877669 by 963.

Advancing to step 1:
2 divided by 963 is 0 with a remainder of 2.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 2 to get 2.
Grab the next digit (8) from the dividend, add it to 2, then carry on: 28 / 963

Moving on to step 2:
28 divided by 963 is 0 with a remainder of 28.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtract 0 from 28 to get 28.
Fetch the next digit (7) from the dividend, attach it to 28 and continue: 287 / 963

Moving on to step 3:
963 goes into 287 0 times with a remainder of 287.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 287 to get 287.
Append the next digit (7) from the dividend to 287 and continue with: 2877 / 963

Let's proceed to step 4:
963 goes into 2877 2 times with a remainder of 951.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtract 1926 from 2877 to get 951.
Append the next digit (6) from the dividend to 951 and continue with: 9516 / 963

On to step 5:
963 can be fit into 9516 9 times, resulting in a remainder of 849.
Use 9 as the next digit of our solution. 
Result so far: 29.0
Subtracting 8667 from 9516 leaves us with 849.
Take the next digit (6) from the dividend and append it to 849, then repeat: 8496 / 963

Moving on to step 6:
963 goes into 8496 8 times with a remainder of 792.
Put 8 as the next digit of the answer. 
Result so far: 298.0
Deduct 7704 from 8496 and we're left with 792.
Take the next digit (9) from the dividend and append it to 792, then repeat: 7929 / 963

Moving on to step 7:
The number 963 fits into 7929 8 times, leaving a remainder of 225.
Use 8 as the next digit of our solution. 
Result so far: 2988.0
Deduct 7704 from 7929 and we're left with 225.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2250, and continue the process.

Going ahead to step 8:
The number 963 fits into 2250 2 times, leaving a remainder of 324.
The number 2 becomes the next digit in our result. 
Result so far: 2988.2
If we subtract 1926 from 2250, we get 324.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3240, and continue the process.

Advancing to step 9:
When dividing 3240 by 963, we get 3 with a remainder of 351.
The next digit of our result is 3. 
Result so far: 2988.23
Subtract 2889 from 3240 to get 351.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3510, and continue the process.

On to step 10:
963 can be fit into 3510 3 times, resulting in a remainder of 621.
The number 3 becomes the next digit in our result. 
Result so far: 2988.233
Subtract 2889 from 3510 to get 621.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6210, and continue the process.

After the division, we end up with 2988.233 and a remainder of 0.0621.