We're dividing 643090 by 75 
Our goal is to divide 643090 by 75.

Step 1:
When dividing 6 by 75, we get 0 with a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 6, we end up with 6.
Include the next digit (4) from the dividend after 6, then repeat: 64 / 75

Step 2:
When dividing 64 by 75, we get 0 with a remainder of 64.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 64, we get 64.
Grab the next digit (3) from the dividend, add it to 64, then carry on: 643 / 75

Step 3:
643 divided by 75 is 8 with a remainder of 43.
The next digit of our result is 8. 
Result so far: 8.0
Deduct 600 from 643 and we're left with 43.
Grab the next digit (0) from the dividend, add it to 43, then carry on: 430 / 75

Moving on to step 4:
If we divide 430 by 75, we get 5 and a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 85.0
The remainder is 55 after subtracting 375 from 430.
Include the next digit (9) from the dividend after 55, then repeat: 559 / 75

Advancing to step 5:
The number 75 fits into 559 7 times, leaving a remainder of 34.
Put 7 as the next digit of the answer. 
Result so far: 857.0
Deduct 525 from 559 and we're left with 34.
Fetch the next digit (0) from the dividend, attach it to 34 and continue: 340 / 75

Step 6:
75 can be fit into 340 4 times, resulting in a remainder of 40.
The next digit of our result is 4. 
Result so far: 8574.0
Subtracting 300 from 340 leaves us with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Step 7:
When dividing 400 by 75, we get 5 with a remainder of 25.
The next digit of our result is 5. 
Result so far: 8574.5
If we subtract 375 from 400, we get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 8:
The number 75 fits into 250 3 times, leaving a remainder of 25.
Put 3 as the next digit of the answer. 
Result so far: 8574.53
Subtract 225 from 250 to get 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Going ahead to step 9:
If we divide 250 by 75, we get 3 and a remainder of 25.
Write down 3 as next digit of the result. 
Result so far: 8574.533
Deduct 225 from 250 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Our division results in 8574.533 with a remaining 0.0025.