966397 ÷ 953 
We want to divide 966397 by 953.

Going ahead to step 1:
The number 953 fits into 9 0 times, leaving a remainder of 9.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtracting 0 from 9 leaves us with 9.
Grab the next digit (6) from the dividend, add it to 9, then carry on: 96 / 953

On to step 2:
96 divided by 953 is 0 with a remainder of 96.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 96 leaves us with 96.
Bring next digit (6) of the dividend behind the 96 and repeat the process: 966 / 953

Advancing to step 3:
When dividing 966 by 953, we get 1 with a remainder of 13.
Write down 1 as next digit of the result. 
Result so far: 1.0
If we subtract 953 from 966, we get 13.
Append the next digit (3) from the dividend to 13 and continue with: 133 / 953

Let's proceed to step 4:
If we divide 133 by 953, we get 0 and a remainder of 133.
Record the quotient 0 as the next digit in the result. 
Result so far: 10.0
Deduct 0 from 133 and we're left with 133.
Take the next digit (9) from the dividend and append it to 133, then repeat: 1339 / 953

On to step 5:
The number 953 fits into 1339 1 times, leaving a remainder of 386.
Record the quotient 1 as the next digit in the result. 
Result so far: 101.0
Subtract 953 from 1339 to get 386.
Include the next digit (7) from the dividend after 386, then repeat: 3867 / 953

Going ahead to step 6:
3867 divided by 953 is 4 with a remainder of 55.
Record the quotient 4 as the next digit in the result. 
Result so far: 1014.0
If we take 3812 away from 3867, we end up with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Step 7:
If we divide 550 by 953, we get 0 and a remainder of 550.
Put 0 as the next digit of the answer. 
Result so far: 1014.0
The remainder is 550 after subtracting 0 from 550.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5500, and continue the process.

On to step 8:
The number 953 fits into 5500 5 times, leaving a remainder of 735.
Put 5 as the next digit of the answer. 
Result so far: 1014.05
Subtracting 4765 from 5500 leaves us with 735.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7350, and continue the process.

Advancing to step 9:
953 can be fit into 7350 7 times, resulting in a remainder of 679.
Use 7 as the next digit of our solution. 
Result so far: 1014.057
The remainder is 679 after subtracting 6671 from 7350.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6790, and continue the process.

Moving on to step 10:
953 can be fit into 6790 7 times, resulting in a remainder of 119.
Use 7 as the next digit of our solution. 
Result so far: 1014.0577
Deduct 6671 from 6790 and we're left with 119.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1190, and continue the process.

After the division, we end up with 1014.0577 and a remainder of 0.00119.