We're dividing 369511 by 90 
We want to divide 369511 by 90.

Advancing to step 1:
The number 90 fits into 3 0 times, leaving a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 3 after subtracting 0 from 3.
Fetch the next digit (6) from the dividend, attach it to 3 and continue: 36 / 90

Advancing to step 2:
If we divide 36 by 90, we get 0 and a remainder of 36.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 36 after subtracting 0 from 36.
Append the next digit (9) from the dividend to 36 and continue with: 369 / 90

On to step 3:
When dividing 369 by 90, we get 4 with a remainder of 9.
Use 4 as the next digit of our solution. 
Result so far: 4.0
Deduct 360 from 369 and we're left with 9.
Fetch the next digit (5) from the dividend, attach it to 9 and continue: 95 / 90

Step 4:
When dividing 95 by 90, we get 1 with a remainder of 5.
Record the quotient 1 as the next digit in the result. 
Result so far: 41.0
Subtracting 90 from 95 leaves us with 5.
Take the next digit (1) from the dividend and append it to 5, then repeat: 51 / 90

On to step 5:
90 can be fit into 51 0 times, resulting in a remainder of 51.
Record the quotient 0 as the next digit in the result. 
Result so far: 410.0
Subtracting 0 from 51 leaves us with 51.
Append the next digit (1) from the dividend to 51 and continue with: 511 / 90

On to step 6:
511 divided by 90 is 5 with a remainder of 61.
Write down 5 as next digit of the result. 
Result so far: 4105.0
If we take 450 away from 511, we end up with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Step 7:
If we divide 610 by 90, we get 6 and a remainder of 70.
The next digit of our result is 6. 
Result so far: 4105.6
If we subtract 540 from 610, we get 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

On to step 8:
90 goes into 700 7 times with a remainder of 70.
The next digit of our result is 7. 
Result so far: 4105.67
Deduct 630 from 700 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

Going ahead to step 9:
90 can be fit into 700 7 times, resulting in a remainder of 70.
The number 7 becomes the next digit in our result. 
Result so far: 4105.677
Deduct 630 from 700 and we're left with 70.
Since there are no more digits in the dividend, we add a zero to the remainder making it 700, and continue the process.

The final outcome is 4105.677, with a leftover of 0.007.