We divide 360668 by 51
We want to divide 360668 by 51.

Moving on to step 1:
If we divide 3 by 51, we get 0 and a remainder of 3.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 51

On to step 2:
51 goes into 36 0 times with a remainder of 36.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we take 0 away from 36, we end up with 36.
Append the next digit (0) from the dividend to 36 and continue with: 360 / 51

Step 3:
360 divided by 51 is 7 with a remainder of 3.
The next digit of our result is 7. 
Result so far: 7.0
Deduct 357 from 360 and we're left with 3.
Append the next digit (6) from the dividend to 3 and continue with: 36 / 51

Step 4:
51 can be fit into 36 0 times, resulting in a remainder of 36.
Write down 0 as next digit of the result. 
Result so far: 70.0
If we subtract 0 from 36, we get 36.
Fetch the next digit (6) from the dividend, attach it to 36 and continue: 366 / 51

On to step 5:
If we divide 366 by 51, we get 7 and a remainder of 9.
The number 7 becomes the next digit in our result. 
Result so far: 707.0
If we subtract 357 from 366, we get 9.
Fetch the next digit (8) from the dividend, attach it to 9 and continue: 98 / 51

Let's proceed to step 6:
98 divided by 51 is 1 with a remainder of 47.
Use 1 as the next digit of our solution. 
Result so far: 7071.0
The remainder is 47 after subtracting 51 from 98.
Since there are no more digits in the dividend, we add a zero to the remainder making it 470, and continue the process.

On to step 7:
When dividing 470 by 51, we get 9 with a remainder of 11.
Use 9 as the next digit of our solution. 
Result so far: 7071.9
The remainder is 11 after subtracting 459 from 470.
Since there are no more digits in the dividend, we add a zero to the remainder making it 110, and continue the process.

Let's proceed to step 8:
When dividing 110 by 51, we get 2 with a remainder of 8.
Record the quotient 2 as the next digit in the result. 
Result so far: 7071.92
Subtracting 102 from 110 leaves us with 8.
Since there are no more digits in the dividend, we add a zero to the remainder making it 80, and continue the process.

Advancing to step 9:
The number 51 fits into 80 1 times, leaving a remainder of 29.
The next digit of our result is 1. 
Result so far: 7071.921
If we take 51 away from 80, we end up with 29.
Since there are no more digits in the dividend, we add a zero to the remainder making it 290, and continue the process.

Advancing to step 10:
51 goes into 290 5 times with a remainder of 35.
The next digit of our result is 5. 
Result so far: 7071.9215
Subtract 255 from 290 to get 35.
Since there are no more digits in the dividend, we add a zero to the remainder making it 350, and continue the process.

Step 11:
When dividing 350 by 51, we get 6 with a remainder of 44.
Record the quotient 6 as the next digit in the result. 
Result so far: 7071.92156
If we subtract 306 from 350, we get 44.
Since there are no more digits in the dividend, we add a zero to the remainder making it 440, and continue the process.

On to step 12:
51 goes into 440 8 times with a remainder of 32.
Write down 8 as next digit of the result. 
Result so far: 7071.921568
Subtracting 408 from 440 leaves us with 32.
Since there are no more digits in the dividend, we add a zero to the remainder making it 320, and continue the process.

Let's proceed to step 13:
51 can be fit into 320 6 times, resulting in a remainder of 14.
Put 6 as the next digit of the answer. 
Result so far: 7071.9215686
The remainder is 14 after subtracting 306 from 320.
Since there are no more digits in the dividend, we add a zero to the remainder making it 140, and continue the process.

Advancing to step 14:
140 divided by 51 is 2 with a remainder of 38.
The number 2 becomes the next digit in our result. 
Result so far: 7071.92156862
Subtracting 102 from 140 leaves us with 38.
Since there are no more digits in the dividend, we add a zero to the remainder making it 380, and continue the process.

In conclusion, the division gives 7071.92156862 with a balance of 3.8e-08.