Let's divide 403259 by 513
We want to divide 403259 by 513.

Going ahead to step 1:
When dividing 4 by 513, we get 0 with a remainder of 4.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Take the next digit (0) from the dividend and append it to 4, then repeat: 40 / 513

Advancing to step 2:
When dividing 40 by 513, we get 0 with a remainder of 40.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 40 to get 40.
Fetch the next digit (3) from the dividend, attach it to 40 and continue: 403 / 513

Step 3:
513 goes into 403 0 times with a remainder of 403.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 403 and we're left with 403.
Fetch the next digit (2) from the dividend, attach it to 403 and continue: 4032 / 513

Going ahead to step 4:
513 can be fit into 4032 7 times, resulting in a remainder of 441.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Deduct 3591 from 4032 and we're left with 441.
Include the next digit (5) from the dividend after 441, then repeat: 4415 / 513

Let's proceed to step 5:
4415 divided by 513 is 8 with a remainder of 311.
The number 8 becomes the next digit in our result. 
Result so far: 78.0
The remainder is 311 after subtracting 4104 from 4415.
Grab the next digit (9) from the dividend, add it to 311, then carry on: 3119 / 513

Step 6:
If we divide 3119 by 513, we get 6 and a remainder of 41.
Record the quotient 6 as the next digit in the result. 
Result so far: 786.0
Subtracting 3078 from 3119 leaves us with 41.
Since there are no more digits in the dividend, we add a zero to the remainder making it 410, and continue the process.

Moving on to step 7:
The number 513 fits into 410 0 times, leaving a remainder of 410.
The next digit of our result is 0. 
Result so far: 786.0
Subtract 0 from 410 to get 410.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4100, and continue the process.

Step 8:
The number 513 fits into 4100 7 times, leaving a remainder of 509.
Write down 7 as next digit of the result. 
Result so far: 786.07
If we subtract 3591 from 4100, we get 509.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5090, and continue the process.

Let's proceed to step 9:
If we divide 5090 by 513, we get 9 and a remainder of 473.
Use 9 as the next digit of our solution. 
Result so far: 786.079
If we take 4617 away from 5090, we end up with 473.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4730, and continue the process.

Advancing to step 10:
The number 513 fits into 4730 9 times, leaving a remainder of 113.
Record the quotient 9 as the next digit in the result. 
Result so far: 786.0799
The remainder is 113 after subtracting 4617 from 4730.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1130, and continue the process.

The quotient of the division is 786.0799, and the remainder is 0.00113.