We're dividing 637627 by 71 
Let's see how many times 71 fits into 637627.

Step 1:
6 divided by 71 is 0 with 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.
Take the next digit (3) from the dividend and append it to 6, then repeat: 63 / 71

Advancing to step 2:
When dividing 63 by 71, we get 0 with a remainder of 63.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 63, we end up with 63.
Include the next digit (7) from the dividend after 63, then repeat: 637 / 71

On to step 3:
637 divided by 71 is 8 with a remainder of 69.
The next digit of our result is 8. 
Result so far: 8.0
If we subtract 568 from 637, we get 69.
Grab the next digit (6) from the dividend, add it to 69, then carry on: 696 / 71

On to step 4:
If we divide 696 by 71, we get 9 and a remainder of 57.
Use 9 as the next digit of our solution. 
Result so far: 89.0
The remainder is 57 after subtracting 639 from 696.
Bring next digit (2) of the dividend behind the 57 and repeat the process: 572 / 71

Let's proceed to step 5:
If we divide 572 by 71, we get 8 and a remainder of 4.
Record the quotient 8 as the next digit in the result. 
Result so far: 898.0
The remainder is 4 after subtracting 568 from 572.
Bring next digit (7) of the dividend behind the 4 and repeat the process: 47 / 71

On to step 6:
71 can be fit into 47 0 times, resulting in a remainder of 47.
Record the quotient 0 as the next digit in the result. 
Result so far: 8980.0
If we take 0 away from 47, we end up with 47.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

Advancing to step 7:
71 can be fit into 470 6 times, resulting in a remainder of 44.
Record the quotient 6 as the next digit in the result. 
Result so far: 8980.6
The remainder is 44 after subtracting 426 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 8:
71 can be fit into 440 6 times, resulting in a remainder of 14.
The next digit of our result is 6. 
Result so far: 8980.66
Deduct 426 from 440 and we're left 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.

The final result is 8980.66 with a remainder of 0.014.