We look at the division of 81907 by 87 
We're looking to find how many times 87 goes into 81907.

Going ahead to step 1:
When dividing 8 by 87, we get 0 with a remainder of 8.
Put 0 as the next digit of the answer. 
Result so far: 0.0
If we subtract 0 from 8, we get 8.
Bring next digit (1) of the dividend behind the 8 and repeat the process: 81 / 87

Let's proceed to step 2:
87 goes into 81 0 times with a remainder of 81.
Use 0 as the next digit of our solution. 
Result so far: 0.0
Deduct 0 from 81 and we're left with 81.
Take the next digit (9) from the dividend and append it to 81, then repeat: 819 / 87

Advancing to step 3:
The number 87 fits into 819 9 times, leaving a remainder of 36.
The next digit of our result is 9. 
Result so far: 9.0
Subtracting 783 from 819 leaves us with 36.
Bring next digit (0) of the dividend behind the 36 and repeat the process: 360 / 87

Step 4:
87 goes into 360 4 times with a remainder of 12.
Use 4 as the next digit of our solution. 
Result so far: 94.0
If we subtract 348 from 360, we get 12.
Include the next digit (7) from the dividend after 12, then repeat: 127 / 87

Moving on to step 5:
If we divide 127 by 87, we get 1 and a remainder of 40.
Use 1 as the next digit of our solution. 
Result so far: 941.0
If we take 87 away from 127, 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 6:
87 goes into 400 4 times with a remainder of 52.
Record the quotient 4 as the next digit in the result. 
Result so far: 941.4
If we take 348 away from 400, we end up 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 7:
The number 87 fits into 520 5 times, leaving a remainder of 85.
The number 5 becomes the next digit in our result. 
Result so far: 941.45
Subtract 435 from 520 to get 85.
Since there are no more digits in the dividend, we add a zero to the remainder making it 850, and continue the process.

Step 8:
87 goes into 850 9 times with a remainder of 67.
The number 9 becomes the next digit in our result. 
Result so far: 941.459
Subtracting 783 from 850 leaves us with 67.
Since there are no more digits in the dividend, we add a zero to the remainder making it 670, and continue the process.

Advancing to step 9:
670 divided by 87 is 7 with a remainder of 61.
Use 7 as the next digit of our solution. 
Result so far: 941.4597
Deduct 609 from 670 and we're left with 61.
Since there are no more digits in the dividend, we add a zero to the remainder making it 610, and continue the process.

Going ahead to step 10:
When dividing 610 by 87, we get 7 with a remainder of 1.
The next digit of our result is 7. 
Result so far: 941.45977
Deduct 609 from 610 and we're left with 1.
Since there are no more digits in the dividend, we add a zero to the remainder making it 10, and continue the process.

In conclusion, the division gives 941.45977 with a balance of 1e-06.