259108 ÷ 51 
Our goal is to divide 259108 by 51.

Step 1:
51 can be fit into 2 0 times, resulting in a remainder of 2.
Record the quotient 0 as the next digit in the result. 
Result so far: 0.0
If we subtract 0 from 2, we get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 51

Let's proceed to step 2:
51 can be fit into 25 0 times, resulting in a remainder of 25.
The next digit of our result is 0. 
Result so far: 0.0
Subtract 0 from 25 to get 25.
Take the next digit (9) from the dividend and append it to 25, then repeat: 259 / 51

On to step 3:
51 goes into 259 5 times with a remainder of 4.
Put 5 as the next digit of the answer. 
Result so far: 5.0
Subtracting 255 from 259 leaves us with 4.
Include the next digit (1) from the dividend after 4, then repeat: 41 / 51

Let's proceed to step 4:
51 can be fit into 41 0 times, resulting in a remainder of 41.
The next digit of our result is 0. 
Result so far: 50.0
If we subtract 0 from 41, we get 41.
Take the next digit (0) from the dividend and append it to 41, then repeat: 410 / 51

Advancing to step 5:
410 divided by 51 is 8 with a remainder of 2.
Write down 8 as next digit of the result. 
Result so far: 508.0
If we take 408 away from 410, we end up with 2.
Take the next digit (8) from the dividend and append it to 2, then repeat: 28 / 51

Step 6:
If we divide 28 by 51, we get 0 and a remainder of 28.
The number 0 becomes the next digit in our result. 
Result so far: 5080.0
If we subtract 0 from 28, we get 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Moving on to step 7:
If we divide 280 by 51, we get 5 and a remainder of 25.
Write down 5 as next digit of the result. 
Result so far: 5080.5
Subtracting 255 from 280 leaves us with 25.
Since there are no more digits in the dividend, we add a zero to the remainder making it 250, and continue the process.

Let's proceed to step 8:
If we divide 250 by 51, we get 4 and a remainder of 46.
Use 4 as the next digit of our solution. 
Result so far: 5080.54
The remainder is 46 after subtracting 204 from 250.
Since there are no more digits in the dividend, we add a zero to the remainder making it 460, and continue the process.

Let's proceed to step 9:
51 goes into 460 9 times with a remainder of 1.
Put 9 as the next digit of the answer. 
Result so far: 5080.549
Subtract 459 from 460 to get 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

Step 10:
10 divided by 51 is 0 with a remainder of 10.
Record the quotient 0 as the next digit in the result. 
Result so far: 5080.549
Subtract 0 from 10 to get 10.
Since there are no more digits in the dividend, we add a zero to the remainder making it 100, and continue the process.

Step 11:
The number 51 fits into 100 1 times, leaving a remainder of 49.
The number 1 becomes the next digit in our result. 
Result so far: 5080.54901
Deduct 51 from 100 and we're left with 49.
Since there are no more digits in the dividend, we add a zero to the remainder making it 490, and continue the process.

Advancing to step 12:
The number 51 fits into 490 9 times, leaving a remainder of 31.
The next digit of our result is 9. 
Result so far: 5080.549019
If we subtract 459 from 490, we get 31.
Since there are no more digits in the dividend, we add a zero to the remainder making it 310, and continue the process.

Step 13:
51 goes into 310 6 times with a remainder of 4.
Record the quotient 6 as the next digit in the result. 
Result so far: 5080.5490196
Deduct 306 from 310 and we're left with 4.
Since there are no more digits in the dividend, we add a zero to the remainder making it 40, and continue the process.

On to step 14:
40 divided by 51 is 0 with a remainder of 40.
Use 0 as the next digit of our solution. 
Result so far: 5080.5490196
If we take 0 away from 40, 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.

In conclusion, the division gives 5080.5490196 with a balance of 4e-08.