171965 ÷ 90 
We want to divide 171965 by 90.

Step 1:
The number 90 fits into 1 0 times, leaving a remainder of 1.
Write down 0 as next digit of the result. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Append the next digit (7) from the dividend to 1 and continue with: 17 / 90

On to step 2:
90 can be fit into 17 0 times, resulting in a remainder of 17.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 17 leaves us with 17.
Append the next digit (1) from the dividend to 17 and continue with: 171 / 90

Going ahead to step 3:
The number 90 fits into 171 1 times, leaving a remainder of 81.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we subtract 90 from 171, we get 81.
Fetch the next digit (9) from the dividend, attach it to 81 and continue: 819 / 90

Advancing to step 4:
90 can be fit into 819 9 times, resulting in a remainder of 9.
Put 9 as the next digit of the answer. 
Result so far: 19.0
If we subtract 810 from 819, we get 9.
Fetch the next digit (6) from the dividend, attach it to 9 and continue: 96 / 90

Going ahead to step 5:
When dividing 96 by 90, we get 1 with a remainder of 6.
Use 1 as the next digit of our solution. 
Result so far: 191.0
If we subtract 90 from 96, we get 6.
Bring next digit (5) of the dividend behind the 6 and repeat the process: 65 / 90

Step 6:
When dividing 65 by 90, we get 0 with a remainder of 65.
Put 0 as the next digit of the answer. 
Result so far: 1910.0
Deduct 0 from 65 and we're left with 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

On to step 7:
90 can be fit into 650 7 times, resulting in a remainder of 20.
The next digit of our result is 7. 
Result so far: 1910.7
Subtracting 630 from 650 leaves us 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.

Moving on to step 8:
200 divided by 90 is 2 with a remainder of 20.
Put 2 as the next digit of the answer. 
Result so far: 1910.72
If we take 180 away from 200, we end up 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 9:
90 goes into 200 2 times with a remainder of 20.
Use 2 as the next digit of our solution. 
Result so far: 1910.722
Subtracting 180 from 200 leaves us 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.

In conclusion, the division gives 1910.722 with a balance of 0.002.