19901 divided by 31 
Our goal is to divide 19901 by 31.

On to step 1:
1 divided by 31 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Fetch the next digit (9) from the dividend, attach it to 1 and continue: 19 / 31

Advancing to step 2:
31 can be fit into 19 0 times, resulting in a remainder of 19.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Subtracting 0 from 19 leaves us with 19.
Append the next digit (9) from the dividend to 19 and continue with: 199 / 31

Moving on to step 3:
The number 31 fits into 199 6 times, leaving a remainder of 13.
Use 6 as the next digit of our solution. 
Result so far: 6.0
If we subtract 186 from 199, we get 13.
Fetch the next digit (0) from the dividend, attach it to 13 and continue: 130 / 31

On to step 4:
When dividing 130 by 31, we get 4 with a remainder of 6.
Use 4 as the next digit of our solution. 
Result so far: 64.0
If we subtract 124 from 130, we get 6.
Fetch the next digit (1) from the dividend, attach it to 6 and continue: 61 / 31

Moving on to step 5:
If we divide 61 by 31, we get 1 and a remainder of 30.
The next digit of our result is 1. 
Result so far: 641.0
Subtract 31 from 61 to get 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 6:
31 goes into 300 9 times with a remainder of 21.
The next digit of our result is 9. 
Result so far: 641.9
Subtracting 279 from 300 leaves us with 21.
Since there are no more digits in the dividend, we add a zero to the remainder making it 210, and continue the process.

Going ahead to step 7:
31 goes into 210 6 times with a remainder of 24.
The number 6 becomes the next digit in our result. 
Result so far: 641.96
Deduct 186 from 210 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 8:
The number 31 fits into 240 7 times, leaving a remainder of 23.
Write down 7 as next digit of the result. 
Result so far: 641.967
The remainder is 23 after subtracting 217 from 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 230, and continue the process.

Let's proceed to step 9:
The number 31 fits into 230 7 times, leaving a remainder of 13.
Use 7 as the next digit of our solution. 
Result so far: 641.9677
Subtracting 217 from 230 leaves us with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

In conclusion, the division gives 641.9677 with a balance of 0.00013.