We look at the division of 9874 by 90 
We want to divide 9874 by 90.

Advancing to step 1:
If we divide 9 by 90, we get 0 and a remainder of 9.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 9, we end up with 9.
Bring next digit (8) of the dividend behind the 9 and repeat the process: 98 / 90

Step 2:
If we divide 98 by 90, we get 1 and a remainder of 8.
The next digit of our result is 1. 
Result so far: 1.0
If we subtract 90 from 98, we get 8.
Grab the next digit (7) from the dividend, add it to 8, then carry on: 87 / 90

On to step 3:
87 divided by 90 is 0 with a remainder of 87.
Write down 0 as next digit of the result. 
Result so far: 10.0
If we subtract 0 from 87, we get 87.
Append the next digit (4) from the dividend to 87 and continue with: 874 / 90

Step 4:
The number 90 fits into 874 9 times, leaving a remainder of 64.
Write down 9 as next digit of the result. 
Result so far: 109.0
Deduct 810 from 874 and we're left with 64.
Since there are no more digits in the dividend, we add a zero to the remainder making it 640, and continue the process.

Step 5:
90 goes into 640 7 times with a remainder of 10.
The next digit of our result is 7. 
Result so far: 109.7
Subtracting 630 from 640 leaves us with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Going ahead to step 6:
90 goes into 100 1 times with a remainder of 10.
The next digit of our result is 1. 
Result so far: 109.71
Subtract 90 from 100 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Advancing to step 7:
If we divide 100 by 90, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 109.711
Deduct 90 from 100 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

After the division, we end up with 109.711 and a remainder of 0.001.