We look at the division of 953641 by 31 
Our goal is to divide 953641 by 31.

Advancing to step 1:
9 divided by 31 is 0 with a remainder of 9.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we subtract 0 from 9, we get 9.
Include the next digit (5) from the dividend after 9, then repeat: 95 / 31

Moving on to step 2:
When dividing 95 by 31, we get 3 with a remainder of 2.
The number 3 becomes the next digit in our result. 
Result so far: 3.0
Deduct 93 from 95 and we're left with 2.
Include the next digit (3) from the dividend after 2, then repeat: 23 / 31

On to step 3:
31 goes into 23 0 times with a remainder of 23.
Put 0 as the next digit of the answer. 
Result so far: 30.0
The remainder is 23 after subtracting 0 from 23.
Include the next digit (6) from the dividend after 23, then repeat: 236 / 31

Going ahead to step 4:
The number 31 fits into 236 7 times, leaving a remainder of 19.
Use 7 as the next digit of our solution. 
Result so far: 307.0
Subtracting 217 from 236 leaves us with 19.
Include the next digit (4) from the dividend after 19, then repeat: 194 / 31

Advancing to step 5:
When dividing 194 by 31, we get 6 with a remainder of 8.
Put 6 as the next digit of the answer. 
Result so far: 3076.0
If we take 186 away from 194, we end up with 8.
Take the next digit (1) from the dividend and append it to 8, then repeat: 81 / 31

Step 6:
The number 31 fits into 81 2 times, leaving a remainder of 19.
Write down 2 as next digit of the result. 
Result so far: 30762.0
If we take 62 away from 81, we end up with 19.
Since there are no more digits in the dividend, we add a zero to the remainder making it 190, and continue the process.

Advancing to step 7:
190 divided by 31 is 6 with a remainder of 4.
The number 6 becomes the next digit in our result. 
Result so far: 30762.6
Deduct 186 from 190 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

Moving on to step 8:
31 goes into 40 1 times with a remainder of 9.
Record the quotient 1 as the next digit in the result. 
Result so far: 30762.61
The remainder is 9 after subtracting 31 from 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Let's proceed to step 9:
When dividing 90 by 31, we get 2 with a remainder of 28.
The number 2 becomes the next digit in our result. 
Result so far: 30762.612
If we take 62 away from 90, we end up with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 10:
31 goes into 280 9 times with a remainder of 1.
Record the quotient 9 as the next digit in the result. 
Result so far: 30762.6129
The remainder is 1 after subtracting 279 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Advancing to step 11:
31 goes into 10 0 times with a remainder of 10.
Write down 0 as next digit of the result. 
Result so far: 30762.6129
Subtract 0 from 10 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.

Step 12:
The number 31 fits into 100 3 times, leaving a remainder of 7.
Use 3 as the next digit of our solution. 
Result so far: 30762.612903
Subtracting 93 from 100 leaves us with 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Let's proceed to step 13:
70 divided by 31 is 2 with a remainder of 8.
The number 2 becomes the next digit in our result. 
Result so far: 30762.6129032
Subtracting 62 from 70 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

On to step 14:
31 can be fit into 80 2 times, resulting in a remainder of 18.
The next digit of our result is 2. 
Result so far: 30762.61290322
If we subtract 62 from 80, we get 18.
Since there are no more digits in the dividend, we add a zero to the remainder making it 180, and continue the process.

After the division, we end up with 30762.61290322 and a remainder of 1.8e-08.