We're dividing 803753 by 97 
Let's see how many times 97 fits into 803753.

Going ahead to step 1:
8 divided by 97 is 0 with a remainder of 8.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Bring next digit (0) of the dividend behind the 8 and repeat the process: 80 / 97

Moving on to step 2:
When dividing 80 by 97, we get 0 with a remainder of 80.
Use 0 as the next digit of our solution. 
Result so far: 0.0
The remainder is 80 after subtracting 0 from 80.
Fetch the next digit (3) from the dividend, attach it to 80 and continue: 803 / 97

Let's proceed to step 3:
97 can be fit into 803 8 times, resulting in a remainder of 27.
Put 8 as the next digit of the answer. 
Result so far: 8.0
Subtract 776 from 803 to get 27.
Fetch the next digit (7) from the dividend, attach it to 27 and continue: 277 / 97

Advancing to step 4:
When dividing 277 by 97, we get 2 with a remainder of 83.
The next digit of our result is 2. 
Result so far: 82.0
If we subtract 194 from 277, we get 83.
Fetch the next digit (5) from the dividend, attach it to 83 and continue: 835 / 97

On to step 5:
835 divided by 97 is 8 with a remainder of 59.
Put 8 as the next digit of the answer. 
Result so far: 828.0
Subtract 776 from 835 to get 59.
Take the next digit (3) from the dividend and append it to 59, then repeat: 593 / 97

Moving on to step 6:
97 can be fit into 593 6 times, resulting in a remainder of 11.
Put 6 as the next digit of the answer. 
Result so far: 8286.0
Subtract 582 from 593 to get 11.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Step 7:
The number 97 fits into 110 1 times, leaving a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 8286.1
The remainder is 13 after subtracting 97 from 110.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 8:
97 goes into 130 1 times with a remainder of 33.
Record the quotient 1 as the next digit in the result. 
Result so far: 8286.11
Subtracting 97 from 130 leaves us with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

After the division, we end up with 8286.11 and a remainder of 0.033.