513407 ÷ 97 
We want to divide 513407 by 97.

On to step 1:
97 can be fit into 5 0 times, resulting in a remainder of 5.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 5 to get 5.
Include the next digit (1) from the dividend after 5, then repeat: 51 / 97

Moving on to step 2:
If we divide 51 by 97, we get 0 and a remainder of 51.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
If we take 0 away from 51, we end up with 51.
Fetch the next digit (3) from the dividend, attach it to 51 and continue: 513 / 97

Step 3:
97 goes into 513 5 times with a remainder of 28.
Use 5 as the next digit of our solution. 
Result so far: 5.0
Subtracting 485 from 513 leaves us with 28.
Take the next digit (4) from the dividend and append it to 28, then repeat: 284 / 97

Step 4:
When dividing 284 by 97, we get 2 with a remainder of 90.
Write down 2 as next digit of the result. 
Result so far: 52.0
If we subtract 194 from 284, we get 90.
Fetch the next digit (0) from the dividend, attach it to 90 and continue: 900 / 97

Step 5:
900 divided by 97 is 9 with a remainder of 27.
Use 9 as the next digit of our solution. 
Result so far: 529.0
Subtract 873 from 900 to get 27.
Take the next digit (7) from the dividend and append it to 27, then repeat: 277 / 97

Advancing to step 6:
97 goes into 277 2 times with a remainder of 83.
Write down 2 as next digit of the result. 
Result so far: 5292.0
Deduct 194 from 277 and we're left with 83.
Since there are no more digits in the dividend, we add a zero to the remainder making it 830, and continue the process.

Advancing to step 7:
The number 97 fits into 830 8 times, leaving a remainder of 54.
Record the quotient 8 as the next digit in the result. 
Result so far: 5292.8
If we take 776 away from 830, we end up with 54.
Since there are no more digits in the dividend, we add a zero to the remainder making it 540, and continue the process.

Step 8:
The number 97 fits into 540 5 times, leaving a remainder of 55.
Put 5 as the next digit of the answer. 
Result so far: 5292.85
Subtracting 485 from 540 leaves us with 55.
Since there are no more digits in the dividend, we add a zero to the remainder making it 550, and continue the process.

Let's proceed to step 9:
If we divide 550 by 97, we get 5 and a remainder of 65.
The next digit of our result is 5. 
Result so far: 5292.855
Subtract 485 from 550 to get 65.
Since there are no more digits in the dividend, we add a zero to the remainder making it 650, and continue the process.

In conclusion, the division gives 5292.855 with a balance of 0.0065.