We divide 643111 by 84
We want to figure out the number of times 643111 can be divided by 84.

Advancing to step 1:
The number 84 fits into 6 0 times, leaving a remainder of 6.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 6 to get 6.
Take the next digit (4) from the dividend and append it to 6, then repeat: 64 / 84

Let's proceed to step 2:
When dividing 64 by 84, we get 0 with a remainder of 64.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 64, we end up with 64.
Fetch the next digit (3) from the dividend, attach it to 64 and continue: 643 / 84

Step 3:
The number 84 fits into 643 7 times, leaving a remainder of 55.
Use 7 as the next digit of our solution. 
Result so far: 7.0
Deduct 588 from 643 and we're left with 55.
Bring next digit (1) of the dividend behind the 55 and repeat the process: 551 / 84

Moving on to step 4:
84 goes into 551 6 times with a remainder of 47.
Use 6 as the next digit of our solution. 
Result so far: 76.0
Deduct 504 from 551 and we're left with 47.
Append the next digit (1) from the dividend to 47 and continue with: 471 / 84

On to step 5:
When dividing 471 by 84, we get 5 with a remainder of 51.
The next digit of our result is 5. 
Result so far: 765.0
Deduct 420 from 471 and we're left with 51.
Include the next digit (1) from the dividend after 51, then repeat: 511 / 84

Step 6:
84 can be fit into 511 6 times, resulting in a remainder of 7.
Record the quotient 6 as the next digit in the result. 
Result so far: 7656.0
The remainder is 7 after subtracting 504 from 511.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Step 7:
84 can be fit into 70 0 times, resulting in a remainder of 70.
Write down 0 as next digit of the result. 
Result so far: 7656.0
The remainder is 70 after subtracting 0 from 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Step 8:
If we divide 700 by 84, we get 8 and a remainder of 28.
Use 8 as the next digit of our solution. 
Result so far: 7656.08
The remainder is 28 after subtracting 672 from 700.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Going ahead to step 9:
When dividing 280 by 84, we get 3 with a remainder of 28.
The number 3 becomes the next digit in our result. 
Result so far: 7656.083
If we take 252 away from 280, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 10:
84 can be fit into 280 3 times, resulting in a remainder of 28.
Write down 3 as next digit of the result. 
Result so far: 7656.0833
Deduct 252 from 280 and we're left with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

After the division, we end up with 7656.0833 and a remainder of 0.00028.