Let's divide 654583 by 71
Our goal is to divide 654583 by 71.

On to step 1:
71 can be fit into 6 0 times, resulting in a remainder of 6.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 71

Step 2:
When dividing 65 by 71, we get 0 with a remainder of 65.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 65, we end up with 65.
Fetch the next digit (4) from the dividend, attach it to 65 and continue: 654 / 71

Going ahead to step 3:
71 can be fit into 654 9 times, resulting in a remainder of 15.
Put 9 as the next digit of the answer. 
Result so far: 9.0
Deduct 639 from 654 and we're left with 15.
Grab the next digit (5) from the dividend, add it to 15, then carry on: 155 / 71

Step 4:
71 can be fit into 155 2 times, resulting in a remainder of 13.
Use 2 as the next digit of our solution. 
Result so far: 92.0
Deduct 142 from 155 and we're left with 13.
Take the next digit (8) from the dividend and append it to 13, then repeat: 138 / 71

Advancing to step 5:
If we divide 138 by 71, we get 1 and a remainder of 67.
Record the quotient 1 as the next digit in the result. 
Result so far: 921.0
If we take 71 away from 138, we end up with 67.
Grab the next digit (3) from the dividend, add it to 67, then carry on: 673 / 71

Let's proceed to step 6:
71 can be fit into 673 9 times, resulting in a remainder of 34.
Write down 9 as next digit of the result. 
Result so far: 9219.0
If we take 639 away from 673, we end up with 34.
Since there are no more digits in the dividend, we add a zero to the remainder making it 340, and continue the process.

On to step 7:
71 goes into 340 4 times with a remainder of 56.
The next digit of our result is 4. 
Result so far: 9219.4
The remainder is 56 after subtracting 284 from 340.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Going ahead to step 8:
When dividing 560 by 71, we get 7 with a remainder of 63.
Put 7 as the next digit of the answer. 
Result so far: 9219.47
Subtract 497 from 560 to get 63.
Since there are no more digits in the dividend, we add a zero to the remainder making it 630, and continue the process.

Going ahead to step 9:
71 can be fit into 630 8 times, resulting in a remainder of 62.
The next digit of our result is 8. 
Result so far: 9219.478
If we subtract 568 from 630, we get 62.
Since there are no more digits in the dividend, we add a zero to the remainder making it 620, and continue the process.

Advancing to step 10:
If we divide 620 by 71, we get 8 and a remainder of 52.
Use 8 as the next digit of our solution. 
Result so far: 9219.4788
If we take 568 away from 620, we end up with 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 9219.4788 with a balance of 0.00052.