430511 ÷ 97 
We want to divide 430511 by 97.

On to step 1:
97 can be fit into 4 0 times, resulting in a remainder of 4.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 4 after subtracting 0 from 4.
Grab the next digit (3) from the dividend, add it to 4, then carry on: 43 / 97

On to step 2:
97 can be fit into 43 0 times, resulting in a remainder of 43.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 43, we end up with 43.
Take the next digit (0) from the dividend and append it to 43, then repeat: 430 / 97

Let's proceed to step 3:
If we divide 430 by 97, we get 4 and a remainder of 42.
The next digit of our result is 4. 
Result so far: 4.0
Subtracting 388 from 430 leaves us with 42.
Bring next digit (5) of the dividend behind the 42 and repeat the process: 425 / 97

Moving on to step 4:
97 can be fit into 425 4 times, resulting in a remainder of 37.
The number 4 becomes the next digit in our result. 
Result so far: 44.0
The remainder is 37 after subtracting 388 from 425.
Grab the next digit (1) from the dividend, add it to 37, then carry on: 371 / 97

Advancing to step 5:
When dividing 371 by 97, we get 3 with a remainder of 80.
The number 3 becomes the next digit in our result. 
Result so far: 443.0
Subtracting 291 from 371 leaves us with 80.
Bring next digit (1) of the dividend behind the 80 and repeat the process: 801 / 97

On to step 6:
The number 97 fits into 801 8 times, leaving a remainder of 25.
Write down 8 as next digit of the result. 
Result so far: 4438.0
Deduct 776 from 801 and we're left with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

On to step 7:
97 goes into 250 2 times with a remainder of 56.
The number 2 becomes the next digit in our result. 
Result so far: 4438.2
If we subtract 194 from 250, we get 56.
Since there are no more digits in the dividend, we add a zero to the remainder making it 560, and continue the process.

Let's proceed to step 8:
When dividing 560 by 97, we get 5 with a remainder of 75.
The number 5 becomes the next digit in our result. 
Result so far: 4438.25
Subtracting 485 from 560 leaves us with 75.
Since there are no more digits in the dividend, we add a zero to the remainder making it 750, and continue the process.

Moving on to step 9:
If we divide 750 by 97, we get 7 and a remainder of 71.
Use 7 as the next digit of our solution. 
Result so far: 4438.257
If we take 679 away from 750, we end up with 71.
Since there are no more digits in the dividend, we add a zero to the remainder making it 710, and continue the process.

Let's proceed to step 10:
710 divided by 97 is 7 with a remainder of 31.
Record the quotient 7 as the next digit in the result. 
Result so far: 4438.2577
Deduct 679 from 710 and we're left with 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

In conclusion, the division gives 4438.2577 with a balance of 0.00031.