678603 ÷ 71 
Let's see how many times 71 fits into 678603.

Advancing to step 1:
71 goes into 6 0 times with a remainder of 6.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (7) from the dividend to 6 and continue with: 67 / 71

Moving on to step 2:
When dividing 67 by 71, we get 0 with a remainder of 67.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 67 to get 67.
Bring next digit (8) of the dividend behind the 67 and repeat the process: 678 / 71

Moving on to step 3:
The number 71 fits into 678 9 times, leaving a remainder of 39.
The next digit of our result is 9. 
Result so far: 9.0
If we take 639 away from 678, we end up with 39.
Fetch the next digit (6) from the dividend, attach it to 39 and continue: 396 / 71

Advancing to step 4:
When dividing 396 by 71, we get 5 with a remainder of 41.
Put 5 as the next digit of the answer. 
Result so far: 95.0
Subtract 355 from 396 to get 41.
Fetch the next digit (0) from the dividend, attach it to 41 and continue: 410 / 71

Advancing to step 5:
71 goes into 410 5 times with a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 955.0
Subtract 355 from 410 to get 55.
Fetch the next digit (3) from the dividend, attach it to 55 and continue: 553 / 71

Advancing to step 6:
71 can be fit into 553 7 times, resulting in a remainder of 56.
The number 7 becomes the next digit in our result. 
Result so far: 9557.0
If we take 497 away from 553, we end up with 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 7:
71 goes into 560 7 times with a remainder of 63.
The number 7 becomes the next digit in our result. 
Result so far: 9557.7
The remainder is 63 after subtracting 497 from 560.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Step 8:
The number 71 fits into 630 8 times, leaving a remainder of 62.
The next digit of our result is 8. 
Result so far: 9557.78
Subtracting 568 from 630 leaves us with 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

On to step 9:
71 can be fit into 620 8 times, resulting in a remainder of 52.
Write down 8 as next digit of the result. 
Result so far: 9557.788
Subtract 568 from 620 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

In conclusion, the division gives 9557.788 with a balance of 0.0052.