We're dividing 337875 by 27 
We're looking to find how many times 27 goes into 337875.

Step 1:
27 goes into 3 0 times with a remainder of 3.
The next digit of our result is 0. 
Result so far: 0.0
Deduct 0 from 3 and we're left with 3.
Fetch the next digit (3) from the dividend, attach it to 3 and continue: 33 / 27

On to step 2:
27 can be fit into 33 1 times, resulting in a remainder of 6.
Put 1 as the next digit of the answer. 
Result so far: 1.0
Deduct 27 from 33 and we're left with 6.
Bring next digit (7) of the dividend behind the 6 and repeat the process: 67 / 27

Moving on to step 3:
27 goes into 67 2 times with a remainder of 13.
The next digit of our result is 2. 
Result so far: 12.0
The remainder is 13 after subtracting 54 from 67.
Fetch the next digit (8) from the dividend, attach it to 13 and continue: 138 / 27

Step 4:
27 goes into 138 5 times with a remainder of 3.
Write down 5 as next digit of the result. 
Result so far: 125.0
If we subtract 135 from 138, we get 3.
Bring next digit (7) of the dividend behind the 3 and repeat the process: 37 / 27

Step 5:
If we divide 37 by 27, we get 1 and a remainder of 10.
Record the quotient 1 as the next digit in the result. 
Result so far: 1251.0
Subtract 27 from 37 to get 10.
Include the next digit (5) from the dividend after 10, then repeat: 105 / 27

Step 6:
When dividing 105 by 27, we get 3 with a remainder of 24.
Put 3 as the next digit of the answer. 
Result so far: 12513.0
Deduct 81 from 105 and we're left with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 7:
27 can be fit into 240 8 times, resulting in a remainder of 24.
Record the quotient 8 as the next digit in the result. 
Result so far: 12513.8
If we subtract 216 from 240, we get 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

Moving on to step 8:
If we divide 240 by 27, we get 8 and a remainder of 24.
Write down 8 as next digit of the result. 
Result so far: 12513.88
Subtracting 216 from 240 leaves us with 24.
Since there are no more digits in the dividend, we add a zero to the remainder making it 240, and continue the process.

In conclusion, the division gives 12513.88 with a balance of 0.024.