645459 ÷ 71 
Our goal is to divide 645459 by 71.

Going ahead to step 1:
If we divide 6 by 71, we get 0 and a remainder of 6.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtracting 0 from 6 leaves us with 6.
Append the next digit (4) from the dividend to 6 and continue with: 64 / 71

Step 2:
If we divide 64 by 71, we get 0 and a remainder of 64.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtracting 0 from 64 leaves us with 64.
Include the next digit (5) from the dividend after 64, then repeat: 645 / 71

Going ahead to step 3:
When dividing 645 by 71, we get 9 with a remainder of 6.
Put 9 as the next digit of the answer. 
Result so far: 9.0
If we subtract 639 from 645, we get 6.
Include the next digit (4) from the dividend after 6, then repeat: 64 / 71

Step 4:
If we divide 64 by 71, we get 0 and a remainder of 64.
Record the quotient 0 as the next digit in the result. 
Result so far: 90.0
Deduct 0 from 64 and we're left with 64.
Bring next digit (5) of the dividend behind the 64 and repeat the process: 645 / 71

Going ahead to step 5:
If we divide 645 by 71, we get 9 and a remainder of 6.
Use 9 as the next digit of our solution. 
Result so far: 909.0
Subtract 639 from 645 to get 6.
Include the next digit (9) from the dividend after 6, then repeat: 69 / 71

Moving on to step 6:
When dividing 69 by 71, we get 0 with a remainder of 69.
Put 0 as the next digit of the answer. 
Result so far: 9090.0
Subtracting 0 from 69 leaves us 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.

Advancing to step 7:
If we divide 690 by 71, we get 9 and a remainder of 51.
Use 9 as the next digit of our solution. 
Result so far: 9090.9
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.

Going ahead to step 8:
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: 9090.97
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.

Advancing to step 9:
If we divide 130 by 71, we get 1 and a remainder of 59.
The number 1 becomes the next digit in our result. 
Result so far: 9090.971
The remainder is 59 after subtracting 71 from 130.
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 10:
If we divide 590 by 71, we get 8 and a remainder of 22.
Use 8 as the next digit of our solution. 
Result so far: 9090.9718
If we subtract 568 from 590, we 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 11:
71 goes into 220 3 times with a remainder of 7.
Put 3 as the next digit of the answer. 
Result so far: 9090.97183
Subtracting 213 from 220 leaves us 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.

Moving on to step 12:
71 can be fit into 70 0 times, resulting in a remainder of 70.
Use 0 as the next digit of our solution. 
Result so far: 9090.97183
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.

Advancing to step 13:
71 goes into 700 9 times with a remainder of 61.
Write down 9 as next digit of the result. 
Result so far: 9090.9718309
Subtract 639 from 700 to get 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 14:
71 can be fit into 610 8 times, resulting in a remainder of 42.
Use 8 as the next digit of our solution. 
Result so far: 9090.97183098
Deduct 568 from 610 and we're left 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.

In conclusion, the division gives 9090.97183098 with a balance of 4.2e-08.