8936103 ÷ 953 
Our goal is to divide 8936103 by 953.

Let's proceed to step 1:
953 goes into 8 0 times with a remainder of 8.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 8 and we're left with 8.
Fetch the next digit (9) from the dividend, attach it to 8 and continue: 89 / 953

On to step 2:
953 goes into 89 0 times with a remainder of 89.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 89 and we're left with 89.
Bring next digit (3) of the dividend behind the 89 and repeat the process: 893 / 953

On to step 3:
If we divide 893 by 953, we get 0 and a remainder of 893.
The next digit of our result is 0. 
Result so far: 0.0
If we take 0 away from 893, we end up with 893.
Bring next digit (6) of the dividend behind the 893 and repeat the process: 8936 / 953

Step 4:
If we divide 8936 by 953, we get 9 and a remainder of 359.
Record the quotient 9 as the next digit in the result. 
Result so far: 9.0
Subtracting 8577 from 8936 leaves us with 359.
Grab the next digit (1) from the dividend, add it to 359, then carry on: 3591 / 953

Step 5:
The number 953 fits into 3591 3 times, leaving a remainder of 732.
Write down 3 as next digit of the result. 
Result so far: 93.0
Deduct 2859 from 3591 and we're left with 732.
Bring next digit (0) of the dividend behind the 732 and repeat the process: 7320 / 953

Going ahead to step 6:
953 goes into 7320 7 times with a remainder of 649.
Put 7 as the next digit of the answer. 
Result so far: 937.0
Deduct 6671 from 7320 and we're left with 649.
Grab the next digit (3) from the dividend, add it to 649, then carry on: 6493 / 953

Advancing to step 7:
953 goes into 6493 6 times with a remainder of 775.
The next digit of our result is 6. 
Result so far: 9376.0
If we subtract 5718 from 6493, we get 775.
Since there are no more digits in the dividend, we add a zero to the remainder making it 7750, and continue the process.

On to step 8:
When dividing 7750 by 953, we get 8 with a remainder of 126.
Write down 8 as next digit of the result. 
Result so far: 9376.8
Subtracting 7624 from 7750 leaves us with 126.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1260, and continue the process.

Step 9:
When dividing 1260 by 953, we get 1 with a remainder of 307.
Use 1 as the next digit of our solution. 
Result so far: 9376.81
If we subtract 953 from 1260, we get 307.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3070, and continue the process.

Let's proceed to step 10:
953 goes into 3070 3 times with a remainder of 211.
The number 3 becomes the next digit in our result. 
Result so far: 9376.813
Deduct 2859 from 3070 and we're left with 211.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2110, and continue the process.

Moving on to step 11:
953 goes into 2110 2 times with a remainder of 204.
Put 2 as the next digit of the answer. 
Result so far: 9376.8132
Subtracting 1906 from 2110 leaves us with 204.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2040, and continue the process.

Let's proceed to step 12:
953 goes into 2040 2 times with a remainder of 134.
The number 2 becomes the next digit in our result. 
Result so far: 9376.81322
Subtracting 1906 from 2040 leaves us with 134.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1340, and continue the process.

The final outcome is 9376.81322, with a leftover of 0.000134.