640819 ÷ 71 
Our goal is to divide 640819 by 71.

Let's proceed to step 1:
The number 71 fits into 6 0 times, leaving a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Fetch the next digit (4) from the dividend, attach it to 6 and continue: 64 / 71

Moving on to step 2:
64 divided by 71 is 0 with a remainder of 64.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtract 0 from 64 to get 64.
Append the next digit (0) from the dividend to 64 and continue with: 640 / 71

On to step 3:
If we divide 640 by 71, we get 9 and a remainder of 1.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
If we take 639 away from 640, we end up with 1.
Append the next digit (8) from the dividend to 1 and continue with: 18 / 71

Let's proceed to step 4:
When dividing 18 by 71, we get 0 with a remainder of 18.
Record the quotient 0 as the next digit in the result. 
Result so far: 90.0
Subtracting 0 from 18 leaves us with 18.
Include the next digit (1) from the dividend after 18, then repeat: 181 / 71

Advancing to step 5:
71 can be fit into 181 2 times, resulting in a remainder of 39.
The next digit of our result is 2. 
Result so far: 902.0
Subtract 142 from 181 to get 39.
Take the next digit (9) from the dividend and append it to 39, then repeat: 399 / 71

Let's proceed to step 6:
71 can be fit into 399 5 times, resulting in a remainder of 44.
Use 5 as the next digit of our solution. 
Result so far: 9025.0
Subtracting 355 from 399 leaves us with 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Moving on to step 7:
440 divided by 71 is 6 with a remainder of 14.
Use 6 as the next digit of our solution. 
Result so far: 9025.6
If we take 426 away from 440, we end up with 14.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Going ahead to step 8:
71 can be fit into 140 1 times, resulting in a remainder of 69.
Record the quotient 1 as the next digit in the result. 
Result so far: 9025.61
If we take 71 away from 140, we end up with 69.
Since there are no more digits in the dividend, we add a zero to the remainder making it 690, and continue the process.

Moving on to step 9:
71 can be fit into 690 9 times, resulting in a remainder of 51.
Use 9 as the next digit of our solution. 
Result so far: 9025.619
Subtract 639 from 690 to get 51.
Since there are no more digits in the dividend, we add a zero to the remainder making it 510, and continue the process.

Step 10:
If we divide 510 by 71, we get 7 and a remainder of 13.
Record the quotient 7 as the next digit in the result. 
Result so far: 9025.6197
If we take 497 away from 510, we end up with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Moving on to step 11:
130 divided by 71 is 1 with a remainder of 59.
The number 1 becomes the next digit in our result. 
Result so far: 9025.61971
If we take 71 away from 130, we end up with 59.
Since there are no more digits in the dividend, we add a zero to the remainder making it 590, and continue the process.

Let's proceed to step 12:
590 divided by 71 is 8 with a remainder of 22.
Put 8 as the next digit of the answer. 
Result so far: 9025.619718
The remainder is 22 after subtracting 568 from 590.
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 13:
71 goes into 220 3 times with a remainder of 7.
Record the quotient 3 as the next digit in the result. 
Result so far: 9025.6197183
If we subtract 213 from 220, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

On to step 14:
71 can be fit into 70 0 times, resulting in a remainder of 70.
Put 0 as the next digit of the answer. 
Result so far: 9025.6197183
The remainder is 70 after subtracting 0 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Our division results in 9025.6197183 with a remaining 7e-08.