We look at the division of 513000 by 53 
Our goal is to divide 513000 by 53.

Going ahead to step 1:
If we divide 5 by 53, we get 0 and a remainder of 5.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
The remainder is 5 after subtracting 0 from 5.
Fetch the next digit (1) from the dividend, attach it to 5 and continue: 51 / 53

Moving on to step 2:
53 goes into 51 0 times with a remainder of 51.
The next digit of our result is 0. 
Result so far: 0.0
If we subtract 0 from 51, we get 51.
Take the next digit (3) from the dividend and append it to 51, then repeat: 513 / 53

Step 3:
If we divide 513 by 53, we get 9 and a remainder of 36.
The number 9 becomes the next digit in our result. 
Result so far: 9.0
Subtract 477 from 513 to get 36.
Grab the next digit (0) from the dividend, add it to 36, then carry on: 360 / 53

Step 4:
360 divided by 53 is 6 with a remainder of 42.
The number 6 becomes the next digit in our result. 
Result so far: 96.0
Subtract 318 from 360 to get 42.
Bring next digit (0) of the dividend behind the 42 and repeat the process: 420 / 53

Advancing to step 5:
420 divided by 53 is 7 with a remainder of 49.
The number 7 becomes the next digit in our result. 
Result so far: 967.0
The remainder is 49 after subtracting 371 from 420.
Append the next digit (0) from the dividend to 49 and continue with: 490 / 53

Moving on to step 6:
The number 53 fits into 490 9 times, leaving a remainder of 13.
Use 9 as the next digit of our solution. 
Result so far: 9679.0
The remainder is 13 after subtracting 477 from 490.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Step 7:
If we divide 130 by 53, we get 2 and a remainder of 24.
The next digit of our result is 2. 
Result so far: 9679.2
If we subtract 106 from 130, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Let's proceed to step 8:
The number 53 fits into 240 4 times, leaving a remainder of 28.
Put 4 as the next digit of the answer. 
Result so far: 9679.24
Subtracting 212 from 240 leaves us with 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Advancing to step 9:
53 can be fit into 280 5 times, resulting in a remainder of 15.
Write down 5 as next digit of the result. 
Result so far: 9679.245
The remainder is 15 after subtracting 265 from 280.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Going ahead to step 10:
53 can be fit into 150 2 times, resulting in a remainder of 44.
The number 2 becomes the next digit in our result. 
Result so far: 9679.2452
The remainder is 44 after subtracting 106 from 150.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

Advancing to step 11:
53 goes into 440 8 times with a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 9679.24528
Deduct 424 from 440 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Moving on to step 12:
When dividing 160 by 53, we get 3 with a remainder of 1.
Write down 3 as next digit of the result. 
Result so far: 9679.245283
If we take 159 away from 160, we end up with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Moving on to step 13:
When dividing 10 by 53, we get 0 with a remainder of 10.
Use 0 as the next digit of our solution. 
Result so far: 9679.245283
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Let's proceed to step 14:
53 can be fit into 100 1 times, resulting in a remainder of 47.
Put 1 as the next digit of the answer. 
Result so far: 9679.24528301
The remainder is 47 after subtracting 53 from 100.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

The final result is 9679.24528301 with a remainder of 4.7e-08.