We divide 513575 by 65
Our goal is to divide 513575 by 65.

On to step 1:
When dividing 5 by 65, we get 0 with a remainder of 5.
Write down 0 as next digit of the result. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 65

Step 2:
65 can be fit into 51 0 times, resulting in a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Bring next digit (3) of the dividend behind the 51 and repeat the process: 513 / 65

On to step 3:
65 goes into 513 7 times with a remainder of 58.
Record the quotient 7 as the next digit in the result. 
Result so far: 7.0
If we take 455 away from 513, we end up with 58.
Append the next digit (5) from the dividend to 58 and continue with: 585 / 65

Let's proceed to step 4:
If we divide 585 by 65, we get 9 and a remainder of 0.
The number 9 becomes the next digit in our result. 
Result so far: 79.0
The remainder is 0 after subtracting 585 from 585.
Take the next digit (7) from the dividend and append it to 0, then repeat: 7 / 65

Moving on to step 5:
When dividing 7 by 65, we get 0 with a remainder of 7.
Write down 0 as next digit of the result. 
Result so far: 790.0
If we subtract 0 from 7, we get 7.
Grab the next digit (5) from the dividend, add it to 7, then carry on: 75 / 65

Going ahead to step 6:
75 divided by 65 is 1 with a remainder of 10.
The number 1 becomes the next digit in our result. 
Result so far: 7901.0
If we subtract 65 from 75, we get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 7:
The number 65 fits into 100 1 times, leaving a remainder of 35.
Record the quotient 1 as the next digit in the result. 
Result so far: 7901.1
Deduct 65 from 100 and we're left with 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Let's proceed to step 8:
The number 65 fits into 350 5 times, leaving a remainder of 25.
Record the quotient 5 as the next digit in the result. 
Result so far: 7901.15
Subtract 325 from 350 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Step 9:
The number 65 fits into 250 3 times, leaving a remainder of 55.
Record the quotient 3 as the next digit in the result. 
Result so far: 7901.153
Subtracting 195 from 250 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Advancing to step 10:
If we divide 550 by 65, we get 8 and a remainder of 30.
Write down 8 as next digit of the result. 
Result so far: 7901.1538
Deduct 520 from 550 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 11:
300 divided by 65 is 4 with a remainder of 40.
Put 4 as the next digit of the answer. 
Result so far: 7901.15384
The remainder is 40 after subtracting 260 from 300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Advancing to step 12:
If we divide 400 by 65, we get 6 and a remainder of 10.
The next digit of our result is 6. 
Result so far: 7901.153846
The remainder is 10 after subtracting 390 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 13:
When dividing 100 by 65, we get 1 with a remainder of 35.
Record the quotient 1 as the next digit in the result. 
Result so far: 7901.1538461
Subtract 65 from 100 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Moving on to step 14:
65 can be fit into 350 5 times, resulting in a remainder of 25.
Use 5 as the next digit of our solution. 
Result so far: 7901.15384615
The remainder is 25 after subtracting 325 from 350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

The final outcome is 7901.15384615, with a leftover of 2.5e-08.