We look at the division of 510945 by 90 
Let's see how many times 90 fits into 510945.

Going ahead to step 1:
If we divide 5 by 90, we get 0 and a remainder of 5.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 90

Going ahead to step 2:
When dividing 51 by 90, we get 0 with a remainder of 51.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 51 leaves us with 51.
Include the next digit (0) from the dividend after 51, then repeat: 510 / 90

Going ahead to step 3:
510 divided by 90 is 5 with a remainder of 60.
Use 5 as the next digit of our solution. 
Result so far: 5.0
If we subtract 450 from 510, we get 60.
Include the next digit (9) from the dividend after 60, then repeat: 609 / 90

Step 4:
When dividing 609 by 90, we get 6 with a remainder of 69.
Record the quotient 6 as the next digit in the result. 
Result so far: 56.0
Subtracting 540 from 609 leaves us with 69.
Fetch the next digit (4) from the dividend, attach it to 69 and continue: 694 / 90

On to step 5:
The number 90 fits into 694 7 times, leaving a remainder of 64.
The next digit of our result is 7. 
Result so far: 567.0
If we subtract 630 from 694, we get 64.
Include the next digit (5) from the dividend after 64, then repeat: 645 / 90

Advancing to step 6:
The number 90 fits into 645 7 times, leaving a remainder of 15.
The next digit of our result is 7. 
Result so far: 5677.0
Subtracting 630 from 645 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Let's proceed to step 7:
90 can be fit into 150 1 times, resulting in a remainder of 60.
The number 1 becomes the next digit in our result. 
Result so far: 5677.1
The remainder is 60 after subtracting 90 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Let's proceed to step 8:
600 divided by 90 is 6 with a remainder of 60.
Put 6 as the next digit of the answer. 
Result so far: 5677.16
Subtracting 540 from 600 leaves us with 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

Moving on to step 9:
If we divide 600 by 90, we get 6 and a remainder of 60.
Use 6 as the next digit of our solution. 
Result so far: 5677.166
Subtract 540 from 600 to get 60.
Since there are no more digits in the dividend, we add a zero to the remainder making it 600, and continue the process.

The final outcome is 5677.166, with a leftover of 0.006.