We're dividing 306781 by 353 
We want to figure out the number of times 306781 can be divided by 353.

Step 1:
353 goes into 3 0 times with a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 3 to get 3.
Bring next digit (0) of the dividend behind the 3 and repeat the process: 30 / 353

Step 2:
The number 353 fits into 30 0 times, leaving a remainder of 30.
Put 0 as the next digit of the answer. 
Result so far: 0.0
Subtract 0 from 30 to get 30.
Take the next digit (6) from the dividend and append it to 30, then repeat: 306 / 353

On to step 3:
When dividing 306 by 353, we get 0 with a remainder of 306.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we subtract 0 from 306, we get 306.
Bring next digit (7) of the dividend behind the 306 and repeat the process: 3067 / 353

Advancing to step 4:
3067 divided by 353 is 8 with a remainder of 243.
Use 8 as the next digit of our solution. 
Result so far: 8.0
If we take 2824 away from 3067, we end up with 243.
Grab the next digit (8) from the dividend, add it to 243, then carry on: 2438 / 353

Let's proceed to step 5:
2438 divided by 353 is 6 with a remainder of 320.
Write down 6 as next digit of the result. 
Result so far: 86.0
If we take 2118 away from 2438, we end up with 320.
Include the next digit (1) from the dividend after 320, then repeat: 3201 / 353

Advancing to step 6:
3201 divided by 353 is 9 with a remainder of 24.
Write down 9 as next digit of the result. 
Result so far: 869.0
If we take 3177 away from 3201, we end up with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 7:
The number 353 fits into 240 0 times, leaving a remainder of 240.
The number 0 becomes the next digit in our result. 
Result so far: 869.0
If we take 0 away from 240, we end up with 240.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2400, and continue the process.

Moving on to step 8:
2400 divided by 353 is 6 with a remainder of 282.
The next digit of our result is 6. 
Result so far: 869.06
Subtract 2118 from 2400 to get 282.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2820, and continue the process.

Let's proceed to step 9:
2820 divided by 353 is 7 with a remainder of 349.
The next digit of our result is 7. 
Result so far: 869.067
The remainder is 349 after subtracting 2471 from 2820.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3490, and continue the process.

Let's proceed to step 10:
353 can be fit into 3490 9 times, resulting in a remainder of 313.
Record the quotient 9 as the next digit in the result. 
Result so far: 869.0679
Deduct 3177 from 3490 and we're left with 313.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3130, and continue the process.

Step 11:
If we divide 3130 by 353, we get 8 and a remainder of 306.
Put 8 as the next digit of the answer. 
Result so far: 869.06798
If we subtract 2824 from 3130, we get 306.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3060, and continue the process.

Moving on to step 12:
3060 divided by 353 is 8 with a remainder of 236.
Use 8 as the next digit of our solution. 
Result so far: 869.067988
Subtracting 2824 from 3060 leaves us with 236.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2360, and continue the process.

The final result is 869.067988 with a remainder of 2.36e-05.