513 ÷ 3 
We're looking to find how many times 3 goes into 513.

Let's proceed to step 1:
5 divided by 3 is 1 with a remainder of 2.
Record the quotient 1 as the next digit in the result. 
Result so far: 1.0
If we subtract 3 from 5, we get 2.
Bring next digit (1) of the dividend behind the 2 and repeat the process: 21 / 3

Step 2:
If we divide 21 by 3, we get 7 and a remainder of 0.
Use 7 as the next digit of our solution. 
Result so far: 17.0
Subtracting 21 from 21 leaves us with 0.
Grab the next digit (3) from the dividend, add it to 0, then carry on: 3 / 3

Step 3:
The number 3 fits into 3 1 times, leaving a remainder of 0.
The next digit of our result is 1. 
Result so far: 171.0
If we take 3 away from 3, we end up with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Step 4:
3 goes into 0 0 times with a remainder of 0.
Record the quotient 0 as the next digit in the result. 
Result so far: 171.0
If we subtract 0 from 0, we get 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

Let's proceed to step 5:
The number 3 fits into 0 0 times, leaving a remainder of 0.
Write down 0 as next digit of the result. 
Result so far: 171.0
Subtracting 0 from 0 leaves us with 0.
Since there are no more digits in the dividend, we add a zero to the remainder making it 0, and continue the process.

In conclusion, the division gives 171.0 with a balance of 0.0.