We divide 340688 by 665
Our goal is to divide 340688 by 665.

Moving on to step 1:
The number 665 fits into 3 0 times, leaving a remainder of 3.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 3, we get 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 665

Advancing to step 2:
If we divide 34 by 665, we get 0 and a remainder of 34.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 34, we end up with 34.
Grab the next digit (0) from the dividend, add it to 34, then carry on: 340 / 665

Advancing to step 3:
If we divide 340 by 665, we get 0 and a remainder of 340.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Subtract 0 from 340 to get 340.
Bring next digit (6) of the dividend behind the 340 and repeat the process: 3406 / 665

On to step 4:
665 goes into 3406 5 times with a remainder of 81.
Use 5 as the next digit of our solution. 
Result so far: 5.0
The remainder is 81 after subtracting 3325 from 3406.
Append the next digit (8) from the dividend to 81 and continue with: 818 / 665

Advancing to step 5:
When dividing 818 by 665, we get 1 with a remainder of 153.
Use 1 as the next digit of our solution. 
Result so far: 51.0
Deduct 665 from 818 and we're left with 153.
Append the next digit (8) from the dividend to 153 and continue with: 1538 / 665

On to step 6:
1538 divided by 665 is 2 with a remainder of 208.
Put 2 as the next digit of the answer. 
Result so far: 512.0
Deduct 1330 from 1538 and we're left with 208.
Since there are no more digits in the dividend, we add a zero to the remainder making it 2080, and continue the process.

Let's proceed to step 7:
The number 665 fits into 2080 3 times, leaving a remainder of 85.
Use 3 as the next digit of our solution. 
Result so far: 512.3
The remainder is 85 after subtracting 1995 from 2080.
Since there are no more digits in the dividend, we add a zero to the remainder making it 850, and continue the process.

Moving on to step 8:
850 divided by 665 is 1 with a remainder of 185.
Put 1 as the next digit of the answer. 
Result so far: 512.31
If we subtract 665 from 850, we get 185.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1850, and continue the process.

On to step 9:
665 can be fit into 1850 2 times, resulting in a remainder of 520.
Use 2 as the next digit of our solution. 
Result so far: 512.312
Subtract 1330 from 1850 to get 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5200, and continue the process.

Going ahead to step 10:
The number 665 fits into 5200 7 times, leaving a remainder of 545.
Record the quotient 7 as the next digit in the result. 
Result so far: 512.3127
If we subtract 4655 from 5200, we get 545.
Since there are no more digits in the dividend, we add a zero to the remainder making it 5450, and continue the process.

On to step 11:
The number 665 fits into 5450 8 times, leaving a remainder of 130.
The number 8 becomes the next digit in our result. 
Result so far: 512.31278
If we subtract 5320 from 5450, we get 130.
Since there are no more digits in the dividend, we add a zero to the remainder making it 1300, and continue the process.

On to step 12:
If we divide 1300 by 665, we get 1 and a remainder of 635.
Put 1 as the next digit of the answer. 
Result so far: 512.312781
The remainder is 635 after subtracting 665 from 1300.
Since there are no more digits in the dividend, we add a zero to the remainder making it 6350, and continue the process.

Step 13:
When dividing 6350 by 665, we get 9 with a remainder of 365.
The next digit of our result is 9. 
Result so far: 512.3127819
Subtract 5985 from 6350 to get 365.
Since there are no more digits in the dividend, we add a zero to the remainder making it 3650, and continue the process.

Moving on to step 14:
3650 divided by 665 is 5 with a remainder of 325.
Use 5 as the next digit of our solution. 
Result so far: 512.31278195
Deduct 3325 from 3650 and we're left 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.

Our division results in 512.31278195 with a remaining 3.25e-07.