We're dividing 7725655 by 513 
We want to figure out the number of times 7725655 can be divided by 513.

Let's proceed to step 1:
513 goes into 7 0 times with a remainder of 7.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 7, we get 7.
Append the next digit (7) from the dividend to 7 and continue with: 77 / 513

Let's proceed to step 2:
The number 513 fits into 77 0 times, leaving a remainder of 77.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 77 leaves us with 77.
Fetch the next digit (2) from the dividend, attach it to 77 and continue: 772 / 513

On to step 3:
When dividing 772 by 513, we get 1 with a remainder of 259.
Write down 1 as next digit of the result. 
Result so far: 1.0
The remainder is 259 after subtracting 513 from 772.
Bring next digit (5) of the dividend behind the 259 and repeat the process: 2595 / 513

On to step 4:
When dividing 2595 by 513, we get 5 with a remainder of 30.
The next digit of our result is 5. 
Result so far: 15.0
Subtract 2565 from 2595 to get 30.
Grab the next digit (6) from the dividend, add it to 30, then carry on: 306 / 513

Advancing to step 5:
513 can be fit into 306 0 times, resulting in a remainder of 306.
Put 0 as the next digit of the answer. 
Result so far: 150.0
If we subtract 0 from 306, we get 306.
Take the next digit (5) from the dividend and append it to 306, then repeat: 3065 / 513

Step 6:
3065 divided by 513 is 5 with a remainder of 500.
The number 5 becomes the next digit in our result. 
Result so far: 1505.0
The remainder is 500 after subtracting 2565 from 3065.
Fetch the next digit (5) from the dividend, attach it to 500 and continue: 5005 / 513

Let's proceed to step 7:
The number 513 fits into 5005 9 times, leaving a remainder of 388.
The number 9 becomes the next digit in our result. 
Result so far: 15059.0
If we take 4617 away from 5005, we end up with 388.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3880, and continue the process.

Going ahead to step 8:
The number 513 fits into 3880 7 times, leaving a remainder of 289.
Use 7 as the next digit of our solution. 
Result so far: 15059.7
Subtract 3591 from 3880 to get 289.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2890, and continue the process.

Moving on to step 9:
If we divide 2890 by 513, we get 5 and a remainder of 325.
Write down 5 as next digit of the result. 
Result so far: 15059.75
If we take 2565 away from 2890, we end up with 325.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3250, and continue the process.

Step 10:
If we divide 3250 by 513, we get 6 and a remainder of 172.
The next digit of our result is 6. 
Result so far: 15059.756
If we take 3078 away from 3250, we end up with 172.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1720, and continue the process.

Step 11:
513 goes into 1720 3 times with a remainder of 181.
Write down 3 as next digit of the result. 
Result so far: 15059.7563
Subtract 1539 from 1720 to get 181.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1810, and continue the process.

Advancing to step 12:
513 goes into 1810 3 times with a remainder of 271.
The next digit of our result is 3. 
Result so far: 15059.75633
If we subtract 1539 from 1810, we get 271.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2710, and continue the process.

The final result is 15059.75633 with a remainder of 0.000271.