505739 ÷ 90 
Our goal is to divide 505739 by 90.

Step 1:
5 divided by 90 is 0 with a remainder of 5.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Deduct 0 from 5 and we're left with 5.
Fetch the next digit (0) from the dividend, attach it to 5 and continue: 50 / 90

Step 2:
The number 90 fits into 50 0 times, leaving a remainder of 50.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 50 and we're left with 50.
Grab the next digit (5) from the dividend, add it to 50, then carry on: 505 / 90

Moving on to step 3:
When dividing 505 by 90, we get 5 with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 450 from 505 leaves us with 55.
Grab the next digit (7) from the dividend, add it to 55, then carry on: 557 / 90

Going ahead to step 4:
557 divided by 90 is 6 with a remainder of 17.
The number 6 becomes the next digit in our result. 
Result so far: 56.0
Deduct 540 from 557 and we're left with 17.
Append the next digit (3) from the dividend to 17 and continue with: 173 / 90

Moving on to step 5:
If we divide 173 by 90, we get 1 and a remainder of 83.
Record the quotient 1 as the next digit in the result. 
Result so far: 561.0
Deduct 90 from 173 and we're left with 83.
Bring next digit (9) of the dividend behind the 83 and repeat the process: 839 / 90

Moving on to step 6:
90 goes into 839 9 times with a remainder of 29.
Record the quotient 9 as the next digit in the result. 
Result so far: 5619.0
Deduct 810 from 839 and we're left with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Let's proceed to step 7:
290 divided by 90 is 3 with a remainder of 20.
Put 3 as the next digit of the answer. 
Result so far: 5619.3
Deduct 270 from 290 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Let's proceed to step 8:
90 goes into 200 2 times with a remainder of 20.
The number 2 becomes the next digit in our result. 
Result so far: 5619.32
Deduct 180 from 200 and we're left with 20.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

Advancing to step 9:
When dividing 200 by 90, we get 2 with a remainder of 20.
Put 2 as the next digit of the answer. 
Result so far: 5619.322
The remainder is 20 after subtracting 180 from 200.
Since there are no more digits in the dividend, we add a zero to the remainder making it 200, and continue the process.

After the division, we end up with 5619.322 and a remainder of 0.002.