203362 ÷ 13 
Our goal is to divide 203362 by 13.

Let's proceed to step 1:
2 divided by 13 is 0 with a remainder of 2.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 2 and we're left with 2.
Fetch the next digit (0) from the dividend, attach it to 2 and continue: 20 / 13

Step 2:
When dividing 20 by 13, we get 1 with a remainder of 7.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 13 from 20, we get 7.
Take the next digit (3) from the dividend and append it to 7, then repeat: 73 / 13

Going ahead to step 3:
When dividing 73 by 13, we get 5 with a remainder of 8.
Use 5 as the next digit of our solution. 
Result so far: 15.0
If we subtract 65 from 73, we get 8.
Fetch the next digit (3) from the dividend, attach it to 8 and continue: 83 / 13

Step 4:
83 divided by 13 is 6 with a remainder of 5.
The number 6 becomes the next digit in our result. 
Result so far: 156.0
If we subtract 78 from 83, we get 5.
Bring next digit (6) of the dividend behind the 5 and repeat the process: 56 / 13

Going ahead to step 5:
56 divided by 13 is 4 with a remainder of 4.
Put 4 as the next digit of the answer. 
Result so far: 1564.0
If we subtract 52 from 56, we get 4.
Take the next digit (2) from the dividend and append it to 4, then repeat: 42 / 13

On to step 6:
13 can be fit into 42 3 times, resulting in a remainder of 3.
Use 3 as the next digit of our solution. 
Result so far: 15643.0
Subtract 39 from 42 to get 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 7:
13 can be fit into 30 2 times, resulting in a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 15643.2
If we take 26 away from 30, we end up 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.

Going ahead to step 8:
When dividing 40 by 13, we get 3 with a remainder of 1.
Put 3 as the next digit of the answer. 
Result so far: 15643.23
Subtract 39 from 40 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Let's proceed to step 9:
The number 13 fits into 10 0 times, leaving a remainder of 10.
The number 0 becomes the next digit in our result. 
Result so far: 15643.23
Deduct 0 from 10 and we're left with 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Moving on to step 10:
If we divide 100 by 13, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 15643.2307
Subtracting 91 from 100 leaves us with 9.
Since there are no more digits in the dividend, we add a zero to the remainder making it 90, and continue the process.

Advancing to step 11:
13 goes into 90 6 times with a remainder of 12.
Use 6 as the next digit of our solution. 
Result so far: 15643.23076
If we take 78 away from 90, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

On to step 12:
When dividing 120 by 13, we get 9 with a remainder of 3.
Record the quotient 9 as the next digit in the result. 
Result so far: 15643.230769
If we take 117 away from 120, we end up 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.

Let's proceed to step 13:
13 goes into 30 2 times with a remainder of 4.
The number 2 becomes the next digit in our result. 
Result so far: 15643.2307692
Subtracting 26 from 30 leaves us 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 14:
40 divided by 13 is 3 with a remainder of 1.
The next digit of our result is 3. 
Result so far: 15643.23076923
If we subtract 39 from 40, we get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 15643.23076923 with a balance of 1e-09.