We look at the division of 512441 by 65 
Let's see how many times 65 fits into 512441.

On to step 1:
5 divided by 65 is 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Append the next digit (1) from the dividend to 5 and continue with: 51 / 65

On to step 2:
65 can be fit into 51 0 times, resulting in a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 51 to get 51.
Bring next digit (2) of the dividend behind the 51 and repeat the process: 512 / 65

On to step 3:
When dividing 512 by 65, we get 7 with a remainder of 57.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
If we take 455 away from 512, we end up with 57.
Append the next digit (4) from the dividend to 57 and continue with: 574 / 65

Step 4:
When dividing 574 by 65, we get 8 with a remainder of 54.
Use 8 as the next digit of our solution. 
Result so far: 78.0
Deduct 520 from 574 and we're left with 54.
Append the next digit (4) from the dividend to 54 and continue with: 544 / 65

Moving on to step 5:
The number 65 fits into 544 8 times, leaving a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 788.0
Subtracting 520 from 544 leaves us with 24.
Take the next digit (1) from the dividend and append it to 24, then repeat: 241 / 65

Advancing to step 6:
If we divide 241 by 65, we get 3 and a remainder of 46.
Use 3 as the next digit of our solution. 
Result so far: 7883.0
If we take 195 away from 241, we end up with 46.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Moving on to step 7:
460 divided by 65 is 7 with a remainder of 5.
The next digit of our result is 7. 
Result so far: 7883.7
Subtracting 455 from 460 leaves us with 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Step 8:
The number 65 fits into 50 0 times, leaving a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 7883.7
Subtracting 0 from 50 leaves us with 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

Moving on to step 9:
500 divided by 65 is 7 with a remainder of 45.
Use 7 as the next digit of our solution. 
Result so far: 7883.707
If we take 455 away from 500, we end up with 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Step 10:
The number 65 fits into 450 6 times, leaving a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 7883.7076
The remainder is 60 after subtracting 390 from 450.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Advancing to step 11:
If we divide 600 by 65, we get 9 and a remainder of 15.
Use 9 as the next digit of our solution. 
Result so far: 7883.70769
Subtract 585 from 600 to get 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 12:
150 divided by 65 is 2 with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 7883.707692
Subtract 130 from 150 to get 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 13:
200 divided by 65 is 3 with a remainder of 5.
Put 3 as the next digit of the answer. 
Result so far: 7883.7076923
If we subtract 195 from 200, we get 5.
Since there are no more digits in the dividend, we add a zero to the remainder making it 50, and continue the process.

Going ahead to step 14:
65 goes into 50 0 times with a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 7883.7076923
The remainder is 50 after subtracting 0 from 50.
Since there are no more digits in the dividend, we add a zero to the remainder making it 500, and continue the process.

The final result is 7883.7076923 with a remainder of 5e-08.