We're dividing 137788 by 48 
We want to figure out the number of times 137788 can be divided by 48.

Going ahead to step 1:
1 divided by 48 is 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
Subtracting 0 from 1 leaves us with 1.
Bring next digit (3) of the dividend behind the 1 and repeat the process: 13 / 48

Going ahead to step 2:
The number 48 fits into 13 0 times, leaving a remainder of 13.
Write down 0 as next digit of the result. 
Result so far: 0.0
The remainder is 13 after subtracting 0 from 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 48

Moving on to step 3:
137 divided by 48 is 2 with a remainder of 41.
Use 2 as the next digit of our solution. 
Result so far: 2.0
Subtracting 96 from 137 leaves us with 41.
Fetch the next digit (7) from the dividend, attach it to 41 and continue: 417 / 48

Let's proceed to step 4:
When dividing 417 by 48, we get 8 with a remainder of 33.
Write down 8 as next digit of the result. 
Result so far: 28.0
If we take 384 away from 417, we end up with 33.
Include the next digit (8) from the dividend after 33, then repeat: 338 / 48

Going ahead to step 5:
When dividing 338 by 48, we get 7 with a remainder of 2.
Write down 7 as next digit of the result. 
Result so far: 287.0
Subtract 336 from 338 to get 2.
Fetch the next digit (8) from the dividend, attach it to 2 and continue: 28 / 48

Going ahead to step 6:
48 can be fit into 28 0 times, resulting in a remainder of 28.
Put 0 as the next digit of the answer. 
Result so far: 2870.0
The remainder is 28 after subtracting 0 from 28.
Since there are no more digits in the dividend, we add a zero to the remainder making it 280, and continue the process.

Let's proceed to step 7:
The number 48 fits into 280 5 times, leaving a remainder of 40.
The next digit of our result is 5. 
Result so far: 2870.5
If we take 240 away from 280, 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.

Step 8:
The number 48 fits into 400 8 times, leaving a remainder of 16.
Use 8 as the next digit of our solution. 
Result so far: 2870.58
Subtracting 384 from 400 leaves us with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Going ahead to step 9:
160 divided by 48 is 3 with a remainder of 16.
Record the quotient 3 as the next digit in the result. 
Result so far: 2870.583
If we subtract 144 from 160, we get 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

Let's proceed to step 10:
The number 48 fits into 160 3 times, leaving a remainder of 16.
The number 3 becomes the next digit in our result. 
Result so far: 2870.5833
Deduct 144 from 160 and we're left with 16.
Since there are no more digits in the dividend, we add a zero to the remainder making it 160, and continue the process.

In conclusion, the division gives 2870.5833 with a balance of 0.00016.