Let's divide 513820 by 9
Our goal is to divide 513820 by 9.

Advancing to step 1:
When dividing 5 by 9, we get 0 with a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Grab the next digit (1) from the dividend, add it to 5, then carry on: 51 / 9

Let's proceed to step 2:
51 divided by 9 is 5 with a remainder of 6.
Write down 5 as next digit of the result. 
Result so far: 5.0
Subtracting 45 from 51 leaves us with 6.
Bring next digit (3) of the dividend behind the 6 and repeat the process: 63 / 9

Let's proceed to step 3:
9 goes into 63 7 times with a remainder of 0.
The next digit of our result is 7. 
Result so far: 57.0
Subtract 63 from 63 to get 0.
Take the next digit (8) from the dividend and append it to 0, then repeat: 8 / 9

Let's proceed to step 4:
9 goes into 8 0 times with a remainder of 8.
Write down 0 as next digit of the result. 
Result so far: 570.0
Subtract 0 from 8 to get 8.
Fetch the next digit (2) from the dividend, attach it to 8 and continue: 82 / 9

Advancing to step 5:
If we divide 82 by 9, we get 9 and a remainder of 1.
The next digit of our result is 9. 
Result so far: 5709.0
Deduct 81 from 82 and we're left with 1.
Bring next digit (0) of the dividend behind the 1 and repeat the process: 10 / 9

Advancing to step 6:
If we divide 10 by 9, we get 1 and a remainder of 1.
Write down 1 as next digit of the result. 
Result so far: 57091.0
If we subtract 9 from 10, 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.

Step 7:
9 can be fit into 10 1 times, resulting in a remainder of 1.
Put 1 as the next digit of the answer. 
Result so far: 57091.1
Subtract 9 from 10 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.

On to step 8:
The number 9 fits into 10 1 times, leaving a remainder of 1.
Record the quotient 1 as the next digit in the result. 
Result so far: 57091.11
The remainder is 1 after subtracting 9 from 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

The quotient of the division is 57091.11, and the remainder is 0.001.