We're dividing 137059 by 78 
We want to figure out the number of times 137059 can be divided by 78.

Step 1:
When dividing 1 by 78, we get 0 with a remainder of 1.
The next digit of our result is 0. 
Result so far: 0.0
The remainder is 1 after subtracting 0 from 1.
Fetch the next digit (3) from the dividend, attach it to 1 and continue: 13 / 78

Moving on to step 2:
13 divided by 78 is 0 with a remainder of 13.
The number 0 becomes the next digit in our result. 
Result so far: 0.0
Deduct 0 from 13 and we're left with 13.
Append the next digit (7) from the dividend to 13 and continue with: 137 / 78

Going ahead to step 3:
137 divided by 78 is 1 with a remainder of 59.
Put 1 as the next digit of the answer. 
Result so far: 1.0
If we take 78 away from 137, we end up with 59.
Fetch the next digit (0) from the dividend, attach it to 59 and continue: 590 / 78

Moving on to step 4:
78 can be fit into 590 7 times, resulting in a remainder of 44.
The next digit of our result is 7. 
Result so far: 17.0
The remainder is 44 after subtracting 546 from 590.
Append the next digit (5) from the dividend to 44 and continue with: 445 / 78

On to step 5:
When dividing 445 by 78, we get 5 with a remainder of 55.
Use 5 as the next digit of our solution. 
Result so far: 175.0
Subtract 390 from 445 to get 55.
Grab the next digit (9) from the dividend, add it to 55, then carry on: 559 / 78

Step 6:
The number 78 fits into 559 7 times, leaving a remainder of 13.
The number 7 becomes the next digit in our result. 
Result so far: 1757.0
Deduct 546 from 559 and we're left with 13.
Since there are no more digits in the dividend, we add a zero to the remainder making it 130, and continue the process.

Advancing to step 7:
The number 78 fits into 130 1 times, leaving a remainder of 52.
Use 1 as the next digit of our solution. 
Result so far: 1757.1
Subtracting 78 from 130 leaves us with 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

On to step 8:
If we divide 520 by 78, we get 6 and a remainder of 52.
Use 6 as the next digit of our solution. 
Result so far: 1757.16
The remainder is 52 after subtracting 468 from 520.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

Let's proceed to step 9:
78 goes into 520 6 times with a remainder of 52.
Put 6 as the next digit of the answer. 
Result so far: 1757.166
Subtract 468 from 520 to get 52.
Since there are no more digits in the dividend, we add a zero to the remainder making it 520, and continue the process.

In conclusion, the division gives 1757.166 with a balance of 0.0052.