1063353 ÷ 669 
We want to figure out the number of times 1063353 can be divided by 669.

Going ahead to step 1:
The number 669 fits into 1 0 times, leaving a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 1, we get 1.
Fetch the next digit (0) from the dividend, attach it to 1 and continue: 10 / 669

On to step 2:
The number 669 fits into 10 0 times, leaving a remainder of 10.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 10, we get 10.
Fetch the next digit (6) from the dividend, attach it to 10 and continue: 106 / 669

On to step 3:
When dividing 106 by 669, we get 0 with a remainder of 106.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 106 leaves us with 106.
Grab the next digit (3) from the dividend, add it to 106, then carry on: 1063 / 669

Moving on to step 4:
1063 divided by 669 is 1 with a remainder of 394.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we take 669 away from 1063, we end up with 394.
Append the next digit (3) from the dividend to 394 and continue with: 3943 / 669

Moving on to step 5:
669 can be fit into 3943 5 times, resulting in a remainder of 598.
Put 5 as the next digit of the answer. 
Result so far: 15.0
The remainder is 598 after subtracting 3345 from 3943.
Fetch the next digit (5) from the dividend, attach it to 598 and continue: 5985 / 669

Going ahead to step 6:
5985 divided by 669 is 8 with a remainder of 633.
Put 8 as the next digit of the answer. 
Result so far: 158.0
If we take 5352 away from 5985, we end up with 633.
Bring next digit (3) of the dividend behind the 633 and repeat the process: 6333 / 669

On to step 7:
6333 divided by 669 is 9 with a remainder of 312.
The next digit of our result is 9. 
Result so far: 1589.0
If we take 6021 away from 6333, we end up with 312.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3120, and continue the process.

Let's proceed to step 8:
If we divide 3120 by 669, we get 4 and a remainder of 444.
The number 4 becomes the next digit in our result. 
Result so far: 1589.4
Subtracting 2676 from 3120 leaves us with 444.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4440, and continue the process.

Advancing to step 9:
When dividing 4440 by 669, we get 6 with a remainder of 426.
The next digit of our result is 6. 
Result so far: 1589.46
If we take 4014 away from 4440, we end up with 426.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4260, and continue the process.

Moving on to step 10:
If we divide 4260 by 669, we get 6 and a remainder of 246.
Write down 6 as next digit of the result. 
Result so far: 1589.466
If we take 4014 away from 4260, we end up with 246.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2460, and continue the process.

In conclusion, the division gives 1589.466 with a balance of 0.0246.