We look at the division of 3506376 by 513 
Our goal is to divide 3506376 by 513.

Moving on to step 1:
513 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Grab the next digit (5) from the dividend, add it to 3, then carry on: 35 / 513

Going ahead to step 2:
35 divided by 513 is 0 with a remainder of 35.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 35 and we're left with 35.
Bring next digit (0) of the dividend behind the 35 and repeat the process: 350 / 513

On to step 3:
513 goes into 350 0 times with a remainder of 350.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 350 leaves us with 350.
Append the next digit (6) from the dividend to 350 and continue with: 3506 / 513

Let's proceed to step 4:
513 can be fit into 3506 6 times, resulting in a remainder of 428.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 3078 from 3506, we get 428.
Fetch the next digit (3) from the dividend, attach it to 428 and continue: 4283 / 513

Let's proceed to step 5:
4283 divided by 513 is 8 with a remainder of 179.
The next digit of our result is 8. 
Result so far: 68.0
If we take 4104 away from 4283, we end up with 179.
Include the next digit (7) from the dividend after 179, then repeat: 1797 / 513

Let's proceed to step 6:
1797 divided by 513 is 3 with a remainder of 258.
Write down 3 as next digit of the result. 
Result so far: 683.0
If we take 1539 away from 1797, we end up with 258.
Fetch the next digit (6) from the dividend, attach it to 258 and continue: 2586 / 513

Advancing to step 7:
513 goes into 2586 5 times with a remainder of 21.
Put 5 as the next digit of the answer. 
Result so far: 6835.0
Subtracting 2565 from 2586 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Advancing to step 8:
When dividing 210 by 513, we get 0 with a remainder of 210.
Use 0 as the next digit of our solution. 
Result so far: 6835.0
If we take 0 away from 210, we end up with 210.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2100, and continue the process.

Advancing to step 9:
513 goes into 2100 4 times with a remainder of 48.
Use 4 as the next digit of our solution. 
Result so far: 6835.04
Deduct 2052 from 2100 and we're left with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 10:
The number 513 fits into 480 0 times, leaving a remainder of 480.
Use 0 as the next digit of our solution. 
Result so far: 6835.04
If we take 0 away from 480, we end up with 480.
Since there are no more digits in the dividend, we add a zero to the remainder making it 4800, and continue the process.

Advancing to step 11:
513 can be fit into 4800 9 times, resulting in a remainder of 183.
Put 9 as the next digit of the answer. 
Result so far: 6835.0409
If we take 4617 away from 4800, we end up with 183.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1830, and continue the process.

Let's proceed to step 12:
When dividing 1830 by 513, we get 3 with a remainder of 291.
Put 3 as the next digit of the answer. 
Result so far: 6835.04093
If we subtract 1539 from 1830, we get 291.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2910, and continue the process.

Let's proceed to step 13:
513 can be fit into 2910 5 times, resulting in a remainder of 345.
The number 5 becomes the next digit in our result. 
Result so far: 6835.040935
The remainder is 345 after subtracting 2565 from 2910.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3450, and continue the process.

Moving on to step 14:
If we divide 3450 by 513, we get 6 and a remainder of 372.
Record the quotient 6 as the next digit in the result. 
Result so far: 6835.0409356
Deduct 3078 from 3450 and we're left with 372.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3720, and continue the process.

Moving on to step 15:
3720 divided by 513 is 7 with a remainder of 129.
The number 7 becomes the next digit in our result. 
Result so far: 6835.04093567
If we subtract 3591 from 3720, we get 129.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1290, and continue the process.

The final result is 6835.04093567 with a remainder of 1.29e-07.