We look at the division of 340641 by 55 
We're looking to find how many times 55 goes into 340641.

Let's proceed to step 1:
When dividing 3 by 55, we get 0 with a remainder of 3.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 3, we end up with 3.
Include the next digit (4) from the dividend after 3, then repeat: 34 / 55

Advancing to step 2:
34 divided by 55 is 0 with a remainder of 34.
Use 0 as the next digit of our solution. 
Result so far: 0.0
If we take 0 away from 34, we end up with 34.
Include the next digit (0) from the dividend after 34, then repeat: 340 / 55

Going ahead to step 3:
When dividing 340 by 55, we get 6 with a remainder of 10.
Write down 6 as next digit of the result. 
Result so far: 6.0
The remainder is 10 after subtracting 330 from 340.
Append the next digit (6) from the dividend to 10 and continue with: 106 / 55

Advancing to step 4:
The number 55 fits into 106 1 times, leaving a remainder of 51.
The number 1 becomes the next digit in our result. 
Result so far: 61.0
The remainder is 51 after subtracting 55 from 106.
Append the next digit (4) from the dividend to 51 and continue with: 514 / 55

Let's proceed to step 5:
514 divided by 55 is 9 with a remainder of 19.
The number 9 becomes the next digit in our result. 
Result so far: 619.0
Subtracting 495 from 514 leaves us with 19.
Grab the next digit (1) from the dividend, add it to 19, then carry on: 191 / 55

Advancing to step 6:
When dividing 191 by 55, we get 3 with a remainder of 26.
Write down 3 as next digit of the result. 
Result so far: 6193.0
Subtract 165 from 191 to get 26.
Since there are no more digits in the dividend, we add a zero to the remainder making it 260, and continue the process.

On to step 7:
The number 55 fits into 260 4 times, leaving a remainder of 40.
Use 4 as the next digit of our solution. 
Result so far: 6193.4
Deduct 220 from 260 and we're left with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 8:
When dividing 400 by 55, we get 7 with a remainder of 15.
The next digit of our result is 7. 
Result so far: 6193.47
The remainder is 15 after subtracting 385 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 9:
If we divide 150 by 55, we get 2 and a remainder of 40.
Record the quotient 2 as the next digit in the result. 
Result so far: 6193.472
If we subtract 110 from 150, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

On to step 10:
55 can be fit into 400 7 times, resulting in a remainder of 15.
The number 7 becomes the next digit in our result. 
Result so far: 6193.4727
Deduct 385 from 400 and we're left with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Moving on to step 11:
The number 55 fits into 150 2 times, leaving a remainder of 40.
Put 2 as the next digit of the answer. 
Result so far: 6193.47272
If we subtract 110 from 150, we get 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 12:
The number 55 fits into 400 7 times, leaving a remainder of 15.
Write down 7 as next digit of the result. 
Result so far: 6193.472727
Subtracting 385 from 400 leaves us with 15.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

Advancing to step 13:
If we divide 150 by 55, we get 2 and a remainder of 40.
The number 2 becomes the next digit in our result. 
Result so far: 6193.4727272
If we take 110 away from 150, we end up with 40.
Since there are no more digits in the dividend, we add a zero to the remainder making it 400, and continue the process.

Going ahead to step 14:
55 goes into 400 7 times with a remainder of 15.
Write down 7 as next digit of the result. 
Result so far: 6193.47272727
The remainder is 15 after subtracting 385 from 400.
Since there are no more digits in the dividend, we add a zero to the remainder making it 150, and continue the process.

In conclusion, the division gives 6193.47272727 with a balance of 1.5e-08.