We look at the division of 15353 by 3 
We're looking to find how many times 3 goes into 15353.

On to step 1:
The number 3 fits into 1 0 times, leaving a remainder of 1.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 1, we end up with 1.
Append the next digit (5) from the dividend to 1 and continue with: 15 / 3

Moving on to step 2:
The number 3 fits into 15 5 times, leaving a remainder of 0.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 15 from 15 leaves us with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 3

Moving on to step 3:
When dividing 3 by 3, we get 1 with a remainder of 0.
The number 1 becomes the next digit in our result. 
Result so far: 51.0
Subtract 3 from 3 to get 0.
Include the next digit (5) from the dividend after 0, then repeat: 5 / 3

Advancing to step 4:
3 goes into 5 1 times with a remainder of 2.
Put 1 as the next digit of the answer. 
Result so far: 511.0
If we subtract 3 from 5, we get 2.
Append the next digit (3) from the dividend to 2 and continue with: 23 / 3

On to step 5:
23 divided by 3 is 7 with a remainder of 2.
Put 7 as the next digit of the answer. 
Result so far: 5117.0
Subtract 21 from 23 to 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 6:
The number 3 fits into 20 6 times, leaving a remainder of 2.
The number 6 becomes the next digit in our result. 
Result so far: 5117.6
Deduct 18 from 20 and we're left with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Let's proceed to step 7:
When dividing 20 by 3, we get 6 with a remainder of 2.
Write down 6 as next digit of the result. 
Result so far: 5117.66
If we take 18 away from 20, we end up with 2.
Since there are no more digits in the dividend, we add a zero to the remainder making it 20, and continue the process.

Our division results in 5117.66 with a remaining 0.002.