We're dividing 171781 by 90 
We want to divide 171781 by 90.

Going ahead to step 1:
When dividing 1 by 90, we get 0 with a remainder of 1.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Subtract 0 from 1 to get 1.
Grab the next digit (7) from the dividend, add it to 1, then carry on: 17 / 90

On to step 2:
If we divide 17 by 90, we get 0 and a remainder of 17.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
The remainder is 17 after subtracting 0 from 17.
Fetch the next digit (1) from the dividend, attach it to 17 and continue: 171 / 90

Going ahead to step 3:
If we divide 171 by 90, we get 1 and a remainder of 81.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 81 after subtracting 90 from 171.
Include the next digit (7) from the dividend after 81, then repeat: 817 / 90

Advancing to step 4:
If we divide 817 by 90, we get 9 and a remainder of 7.
Record the quotient 9 as the next digit in the result. 
Result so far: 19.0
Subtract 810 from 817 to get 7.
Take the next digit (8) from the dividend and append it to 7, then repeat: 78 / 90

Moving on to step 5:
90 can be fit into 78 0 times, resulting in a remainder of 78.
Record the quotient 0 as the next digit in the result. 
Result so far: 190.0
If we subtract 0 from 78, we get 78.
Take the next digit (1) from the dividend and append it to 78, then repeat: 781 / 90

Let's proceed to step 6:
90 can be fit into 781 8 times, resulting in a remainder of 61.
Put 8 as the next digit of the answer. 
Result so far: 1908.0
Subtract 720 from 781 to get 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Moving on to step 7:
90 goes into 610 6 times with a remainder of 70.
Record the quotient 6 as the next digit in the result. 
Result so far: 1908.6
Subtracting 540 from 610 leaves us 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.

Moving on to step 8:
The number 90 fits into 700 7 times, leaving a remainder of 70.
Put 7 as the next digit of the answer. 
Result so far: 1908.67
If we subtract 630 from 700, 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.

Let's proceed to step 9:
When dividing 700 by 90, we get 7 with a remainder of 70.
Write down 7 as next digit of the result. 
Result so far: 1908.677
If we take 630 away from 700, we end up 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.

In conclusion, the division gives 1908.677 with a balance of 0.007.