654363 ÷ 51 
Our goal is to divide 654363 by 51.

On to step 1:
51 goes into 6 0 times with a remainder of 6.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 6 after subtracting 0 from 6.
Fetch the next digit (5) from the dividend, attach it to 6 and continue: 65 / 51

Moving on to step 2:
If we divide 65 by 51, we get 1 and a remainder of 14.
The number 1 becomes the next digit in our result. 
Result so far: 1.0
Subtracting 51 from 65 leaves us with 14.
Fetch the next digit (4) from the dividend, attach it to 14 and continue: 144 / 51

Step 3:
51 goes into 144 2 times with a remainder of 42.
Use 2 as the next digit of our solution. 
Result so far: 12.0
If we subtract 102 from 144, we get 42.
Bring next digit (3) of the dividend behind the 42 and repeat the process: 423 / 51

Let's proceed to step 4:
The number 51 fits into 423 8 times, leaving a remainder of 15.
The number 8 becomes the next digit in our result. 
Result so far: 128.0
The remainder is 15 after subtracting 408 from 423.
Grab the next digit (6) from the dividend, add it to 15, then carry on: 156 / 51

Let's proceed to step 5:
51 goes into 156 3 times with a remainder of 3.
The next digit of our result is 3. 
Result so far: 1283.0
Subtracting 153 from 156 leaves us with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 51

Moving on to step 6:
If we divide 33 by 51, we get 0 and a remainder of 33.
Put 0 as the next digit of the answer. 
Result so far: 12830.0
Deduct 0 from 33 and we're left with 33.
Since there are no more digits in the dividend, we add a zero to the remainder making it 330, and continue the process.

Let's proceed to step 7:
51 can be fit into 330 6 times, resulting in a remainder of 24.
Write down 6 as next digit of the result. 
Result so far: 12830.6
The remainder is 24 after subtracting 306 from 330.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Advancing to step 8:
If we divide 240 by 51, we get 4 and a remainder of 36.
The next digit of our result is 4. 
Result so far: 12830.64
If we subtract 204 from 240, we get 36.
Since there are no more digits in the dividend, we add a zero to the remainder making it 360, and continue the process.

Step 9:
When dividing 360 by 51, we get 7 with a remainder of 3.
The next digit of our result is 7. 
Result so far: 12830.647
If we take 357 away from 360, we end up with 3.
Since there are no more digits in the dividend, we add a zero to the remainder making it 30, and continue the process.

Step 10:
When dividing 30 by 51, we get 0 with a remainder of 30.
The number 0 becomes the next digit in our result. 
Result so far: 12830.647
If we take 0 away from 30, we end up with 30.
Since there are no more digits in the dividend, we add a zero to the remainder making it 300, and continue the process.

On to step 11:
51 goes into 300 5 times with a remainder of 45.
Use 5 as the next digit of our solution. 
Result so far: 12830.64705
Subtract 255 from 300 to get 45.
Since there are no more digits in the dividend, we add a zero to the remainder making it 450, and continue the process.

Going ahead to step 12:
450 divided by 51 is 8 with a remainder of 42.
The number 8 becomes the next digit in our result. 
Result so far: 12830.647058
Subtract 408 from 450 to get 42.
Since there are no more digits in the dividend, we add a zero to the remainder making it 420, and continue the process.

Let's proceed to step 13:
The number 51 fits into 420 8 times, leaving a remainder of 12.
Write down 8 as next digit of the result. 
Result so far: 12830.6470588
If we take 408 away from 420, we end up with 12.
Since there are no more digits in the dividend, we add a zero to the remainder making it 120, and continue the process.

In conclusion, the division gives 12830.6470588 with a balance of 1.2e-07.