11338 ÷ 17 
Our goal is to divide 11338 by 17.

Advancing to step 1:
1 divided by 17 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.
Append the next digit (1) from the dividend to 1 and continue with: 11 / 17

On to step 2:
11 divided by 17 is 0 with a remainder of 11.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 11 to get 11.
Take the next digit (3) from the dividend and append it to 11, then repeat: 113 / 17

Going ahead to step 3:
The number 17 fits into 113 6 times, leaving a remainder of 11.
Record the quotient 6 as the next digit in the result. 
Result so far: 6.0
If we take 102 away from 113, we end up with 11.
Grab the next digit (3) from the dividend, add it to 11, then carry on: 113 / 17

On to step 4:
When dividing 113 by 17, we get 6 with a remainder of 11.
Record the quotient 6 as the next digit in the result. 
Result so far: 66.0
If we take 102 away from 113, we end up with 11.
Include the next digit (8) from the dividend after 11, then repeat: 118 / 17

Step 5:
The number 17 fits into 118 6 times, leaving a remainder of 16.
The next digit of our result is 6. 
Result so far: 666.0
The remainder is 16 after subtracting 102 from 118.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 6:
17 can be fit into 160 9 times, resulting in a remainder of 7.
Use 9 as the next digit of our solution. 
Result so far: 666.9
If we subtract 153 from 160, we get 7.
Since there are no more digits in the dividend, we add a zero to the remainder making it 70, and continue the process.

Advancing to step 7:
70 divided by 17 is 4 with a remainder of 2.
Use 4 as the next digit of our solution. 
Result so far: 666.94
If we subtract 68 from 70, we get 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Advancing to step 8:
20 divided by 17 is 1 with a remainder of 3.
Record the quotient 1 as the next digit in the result. 
Result so far: 666.941
Subtracting 17 from 20 leaves us with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 9:
The number 17 fits into 30 1 times, leaving a remainder of 13.
Put 1 as the next digit of the answer. 
Result so far: 666.9411
Subtracting 17 from 30 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.

The final result is 666.9411 with a remainder of 0.00013.