509200 ÷ 71 
We want to figure out the number of times 509200 can be divided by 71.

Step 1:
If we divide 5 by 71, we get 0 and a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 5, we get 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 71

Moving on to step 2:
If we divide 50 by 71, we get 0 and a remainder of 50.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 50 and we're left with 50.
Bring next digit (9) of the dividend behind the 50 and repeat the process: 509 / 71

On to step 3:
509 divided by 71 is 7 with a remainder of 12.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtracting 497 from 509 leaves us with 12.
Fetch the next digit (2) from the dividend, attach it to 12 and continue: 122 / 71

Advancing to step 4:
If we divide 122 by 71, we get 1 and a remainder of 51.
Put 1 as the next digit of the answer. 
Result so far: 71.0
If we subtract 71 from 122, we get 51.
Bring next digit (0) of the dividend behind the 51 and repeat the process: 510 / 71

Moving on to step 5:
The number 71 fits into 510 7 times, leaving a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 717.0
Deduct 497 from 510 and we're left with 13.
Bring next digit (0) of the dividend behind the 13 and repeat the process: 130 / 71

Going ahead to step 6:
71 can be fit into 130 1 times, resulting in a remainder of 59.
The number 1 becomes the next digit in our result. 
Result so far: 7171.0
If we subtract 71 from 130, we get 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Advancing to step 7:
590 divided by 71 is 8 with a remainder of 22.
The next digit of our result is 8. 
Result so far: 7171.8
Subtract 568 from 590 to get 22.
Since there are no more digits in the dividend, we add a zero to the remainder making it 220, and continue the process.

Let's proceed to step 8:
220 divided by 71 is 3 with a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 7171.83
If we take 213 away from 220, we end up with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Going ahead to step 9:
71 goes into 70 0 times with a remainder of 70.
The number 0 becomes the next digit in our result. 
Result so far: 7171.83
Subtracting 0 from 70 leaves us with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 10:
71 can be fit into 700 9 times, resulting in a remainder of 61.
The next digit of our result is 9. 
Result so far: 7171.8309
Deduct 639 from 700 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Step 11:
610 divided by 71 is 8 with a remainder of 42.
Use 8 as the next digit of our solution. 
Result so far: 7171.83098
If we take 568 away from 610, we end up with 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

On to step 12:
If we divide 420 by 71, we get 5 and a remainder of 65.
Record the quotient 5 as the next digit in the result. 
Result so far: 7171.830985
Subtracting 355 from 420 leaves us with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

Moving on to step 13:
If we divide 650 by 71, we get 9 and a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 7171.8309859
If we subtract 639 from 650, we get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Moving on to step 14:
110 divided by 71 is 1 with a remainder of 39.
The number 1 becomes the next digit in our result. 
Result so far: 7171.83098591
If we take 71 away from 110, we end up with 39.
Since there are no more digits in the dividend, we add a zero to the remainder making it 390, and continue the process.

After the division, we end up with 7171.83098591 and a remainder of 3.9e-08.