We look at the division of 641928 by 90 
We're looking to find how many times 90 goes into 641928.

Step 1:
If we divide 6 by 90, we get 0 and a remainder of 6.
Use 0 as the next digit of our solution. 
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 / 90

Let's proceed to step 2:
The number 90 fits into 64 0 times, leaving 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.
Append the next digit (1) from the dividend to 64 and continue with: 641 / 90

On to step 3:
90 can be fit into 641 7 times, resulting in a remainder of 11.
The number 7 becomes the next digit in our result. 
Result so far: 7.0
Subtract 630 from 641 to get 11.
Fetch the next digit (9) from the dividend, attach it to 11 and continue: 119 / 90

Let's proceed to step 4:
119 divided by 90 is 1 with a remainder of 29.
The next digit of our result is 1. 
Result so far: 71.0
The remainder is 29 after subtracting 90 from 119.
Append the next digit (2) from the dividend to 29 and continue with: 292 / 90

Moving on to step 5:
292 divided by 90 is 3 with a remainder of 22.
Use 3 as the next digit of our solution. 
Result so far: 713.0
The remainder is 22 after subtracting 270 from 292.
Bring next digit (8) of the dividend behind the 22 and repeat the process: 228 / 90

On to step 6:
90 goes into 228 2 times with a remainder of 48.
Record the quotient 2 as the next digit in the result. 
Result so far: 7132.0
Subtracting 180 from 228 leaves us with 48.
Since there are no more digits in the dividend, we add a zero to the remainder making it 480, and continue the process.

Step 7:
90 can be fit into 480 5 times, resulting in a remainder of 30.
Use 5 as the next digit of our solution. 
Result so far: 7132.5
If we subtract 450 from 480, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Step 8:
90 goes into 300 3 times with a remainder of 30.
Use 3 as the next digit of our solution. 
Result so far: 7132.53
If we subtract 270 from 300, we get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

Advancing to step 9:
300 divided by 90 is 3 with a remainder of 30.
The number 3 becomes the next digit in our result. 
Result so far: 7132.533
Deduct 270 from 300 and we're left with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

After the division, we end up with 7132.533 and a remainder of 0.003.